कैलकुलस उदाहरण

$\int \sin^{6} (x) d x$

चरण 1

गुणनखंड निकालकर सरलीकृत करें.

और स्टेप्स के लिए टैप करें…

चरण 1.1

$6$ में से $2$ का गुणनखंड करें.

$\int {\sin (x)}^{2 (3)} d x$

चरण 1.2

${\sin (x)}^{2 (3)}$ को घातांक के रूप में फिर से लिखें.

$\int {(\sin^{2} (x))}^{3} d x$

चरण 2

$\sin^{2} (x)$ को $\frac{1 - \cos (2 x)}{2}$ के रूप में फिर से लिखने के लिए अर्ध-कोण सूत्र का प्रयोग करें.

$\int {(\frac{1 - \cos (2 x)}{2})}^{3} d x$

चरण 3

मान लीजिए $u_{1} = 2 x$ .फिर $d u_{1} = 2 d x$ , तो $\frac{1}{2} d u_{1} = d x$ . $u_{1}$ और $d$ $u_{1}$ का उपयोग करके फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 3.1

मान लें $u_{1} = 2 x$ . $\frac{d u_{1}}{d x}$ ज्ञात करें.

और स्टेप्स के लिए टैप करें…

चरण 3.1.1

$2 x$ को अवकलित करें.

$\frac{d}{d x} [2 x]$

चरण 3.1.2

चूंकि $2$ , $x$ के संबंध में स्थिर है, $x$ के संबंध में $2 x$ का व्युत्पन्न $2 \frac{d}{d x} [x]$ है.

$2 \frac{d}{d x} [x]$

चरण 3.1.3

घात नियम का उपयोग करके अवकलन करें, जिसमें यह वर्णन हो कि $\frac{d}{d x} [x^{n}]$ $n x^{n - 1}$ है, जहाँ $n = 1$ है.

$2 \cdot 1$

चरण 3.1.4

$2$ को $1$ से गुणा करें.

$2$

चरण 3.2

$u_{1}$ और $d u_{1}$ का उपयोग करके समस्या को फिर से लिखें.

$\int {(\frac{1 - \cos (u_{1})}{2})}^{3} \frac{1}{2} d u_{1}$

चरण 4

चूँकि $\frac{1}{2}$ बटे $u_{1}$ अचर है, $\frac{1}{2}$ को समाकलन से हटा दें.

$\frac{1}{2} \int {(\frac{1 - \cos (u_{1})}{2})}^{3} d u_{1}$

चरण 5

से गुणा करके सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.1

एक गुणनफल के रूप में $\frac{1 - \cos (u_{1})}{2}$ को फिर से लिखें.

$\frac{1}{2} \int {(\frac{1}{2} \cdot (1 - \cos (u_{1})))}^{3} d u_{1}$

चरण 5.2

${(\frac{1}{2} \cdot (1 - \cos (u_{1})))}^{3}$ का प्रसार करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.1

एक गुणनफल के रूप में घातांक को फिर से लिखें.

$\frac{1}{2} \int \frac{1}{2} \cdot (1 - \cos (u_{1})) {(\frac{1}{2} \cdot (1 - \cos (u_{1})))}^{2} d u_{1}$

चरण 5.2.2

एक गुणनफल के रूप में घातांक को फिर से लिखें.

$\frac{1}{2} \int \frac{1}{2} \cdot (1 - \cos (u_{1})) (\frac{1}{2} \cdot (1 - \cos (u_{1})) (\frac{1}{2} \cdot (1 - \cos (u_{1})))) d u_{1}$

चरण 5.2.3

वितरण गुणधर्म लागू करें.

$\frac{1}{2} \int (\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot (- \cos (u_{1}))) (\frac{1}{2} \cdot (1 - \cos (u_{1})) (\frac{1}{2} \cdot (1 - \cos (u_{1})))) d u_{1}$

चरण 5.2.4

वितरण गुणधर्म लागू करें.

$\frac{1}{2} \int (\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot (- \cos (u_{1}))) ((\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot (- \cos (u_{1}))) (\frac{1}{2} \cdot (1 - \cos (u_{1})))) d u_{1}$

चरण 5.2.5

वितरण गुणधर्म लागू करें.

$\frac{1}{2} \int (\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot (- \cos (u_{1}))) ((\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot (- \cos (u_{1}))) (\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.6

वितरण गुणधर्म लागू करें.

$\frac{1}{2} \int (\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot (- \cos (u_{1}))) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot (- \cos (u_{1}))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.7

वितरण गुणधर्म लागू करें.

$\frac{1}{2} \int (\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot (- \cos (u_{1}))) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1}))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 + \frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.8

वितरण गुणधर्म लागू करें.

चरण 5.2.9

वितरण गुणधर्म लागू करें.

$\frac{1}{2} \int \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1}))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1}))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.10

वितरण गुणधर्म लागू करें.

$\frac{1}{2} \int \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1}))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.11

वितरण गुणधर्म लागू करें.

$\frac{1}{2} \int \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1}))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.12

वितरण गुणधर्म लागू करें.

$\frac{1}{2} \int \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1}))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.13

वितरण गुणधर्म लागू करें.

$\frac{1}{2} \int \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.14

वितरण गुणधर्म लागू करें.

$\frac{1}{2} \int \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.15

वितरण गुणधर्म लागू करें.

$\frac{1}{2} \int \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.16

$\frac{1}{2}$ और $1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot \frac{1}{2} (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.17

$\frac{1}{2}$ और $1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot \frac{1}{2} (1 \cdot \frac{1}{2} (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.18

$\frac{1}{2}$ और $1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot \frac{1}{2} (1 \cdot \frac{1}{2} (1 \cdot \frac{1}{2})) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.19

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot \frac{1}{2} (1 \cdot 1 \frac{1}{2} \cdot \frac{1}{2}) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.20

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot \frac{1}{2} (1 \cdot 1 \frac{1}{2}) \cdot \frac{1}{2} + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.21

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot \frac{1}{2} (1 \cdot 1) \frac{1}{2} \cdot \frac{1}{2} + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.22

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.23

$\frac{1}{2}$ और $1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.24

$\frac{1}{2}$ और $1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (1 \cdot \frac{1}{2} (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.25

$\frac{1}{2}$ और $- 1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (1 \cdot \frac{1}{2} (- 1 \cdot \frac{1}{2} \cos (u_{1}))) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.26

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (1 \cdot \frac{1}{2} (- 1 \cdot \frac{1}{2}) \cos (u_{1})) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.27

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (1 \cdot - 1 \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1})) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.28

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (1 \cdot - 1 \frac{1}{2} \cdot \frac{1}{2}) \cos (u_{1}) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.29

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (1 \cdot - 1 \frac{1}{2}) \cdot \frac{1}{2} \cos (u_{1}) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.30

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (1 \cdot - 1) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.31

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.32

$\frac{1}{2}$ और $1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot \frac{1}{2} (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.33

$\frac{1}{2}$ और $- 1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot \frac{1}{2} (- 1 \cdot \frac{1}{2} \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.34

$\frac{1}{2}$ और $1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot \frac{1}{2} (- 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot \frac{1}{2})) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.35

$\cos (u_{1})$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot \frac{1}{2} (- 1 \cdot \frac{1}{2} \cdot 1 \cos (u_{1}) \cdot \frac{1}{2}) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.36

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot \frac{1}{2} (- 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2}) + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.37

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot \frac{1}{2} (- 1 \cdot 1 \frac{1}{2} \cos (u_{1})) \cdot \frac{1}{2} + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.38

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot \frac{1}{2} (- 1 \cdot 1 \frac{1}{2}) \cos (u_{1}) \cdot \frac{1}{2} + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.39

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot \frac{1}{2} (- 1 \cdot 1) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.40

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + \frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.41

$\frac{1}{2}$ और $1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.42

$\frac{1}{2}$ और $- 1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (- 1 \cdot \frac{1}{2} \cos (u_{1}) (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.43

$\frac{1}{2}$ और $- 1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (- 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot \frac{1}{2} \cos (u_{1}))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.44

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (- 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot \frac{1}{2}) \cos (u_{1})) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.45

$\cos (u_{1})$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (- 1 \cdot \frac{1}{2} \cdot - 1 \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1})) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.46

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (- 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1})) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.47

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (- 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2}) \cos (u_{1}) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.48

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (- 1 \cdot - 1 \frac{1}{2} \cos (u_{1})) \cdot \frac{1}{2} \cos (u_{1}) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.49

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (- 1 \cdot - 1 \frac{1}{2}) \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.50

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot \frac{1}{2} (- 1 \cdot - 1) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.51

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.52

$\frac{1}{2}$ और $- 1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.53

$\frac{1}{2}$ और $1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot \frac{1}{2} (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.54

$\frac{1}{2}$ और $1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot \frac{1}{2} (1 \cdot \frac{1}{2})) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.55

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot 1 \frac{1}{2} \cdot \frac{1}{2}) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.56

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot 1 \frac{1}{2}) \cdot \frac{1}{2} + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.57

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot 1) \frac{1}{2} \cdot \frac{1}{2} + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.58

$\cos (u_{1})$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cdot 1 \cdot 1 \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.59

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.60

$\frac{1}{2}$ और $- 1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (\frac{1}{2} \cdot 1 (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.61

$\frac{1}{2}$ और $1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot \frac{1}{2} (\frac{1}{2} \cdot (- \cos (u_{1})))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.62

$\frac{1}{2}$ और $- 1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot \frac{1}{2} (- 1 \cdot \frac{1}{2} \cos (u_{1}))) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.63

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot \frac{1}{2} (- 1 \cdot \frac{1}{2}) \cos (u_{1})) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.64

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot - 1 \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1})) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.65

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot - 1 \frac{1}{2} \cdot \frac{1}{2}) \cos (u_{1}) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.66

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot - 1 \frac{1}{2}) \cdot \frac{1}{2} \cos (u_{1}) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.67

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot - 1) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.68

$\cos (u_{1})$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cdot 1 \cdot - 1 \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.69

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.70

$\frac{1}{2}$ और $- 1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.71

$\frac{1}{2}$ और $- 1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot \frac{1}{2} \cos (u_{1}) (\frac{1}{2} \cdot 1)) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.72

$\frac{1}{2}$ और $1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot \frac{1}{2} \cos (u_{1}) (1 \cdot \frac{1}{2})) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.73

$\cos (u_{1})$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot \frac{1}{2} \cdot 1 \cos (u_{1}) \cdot \frac{1}{2}) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.74

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2}) + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.75

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot 1 \frac{1}{2} \cos (u_{1})) \cdot \frac{1}{2} + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.76

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot 1 \frac{1}{2}) \cos (u_{1}) \cdot \frac{1}{2} + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.77

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot 1) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.78

$\cos (u_{1})$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot \frac{1}{2} \cdot - 1 \cdot 1 \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.79

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + \frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.80

$\frac{1}{2}$ और $- 1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (\frac{1}{2} \cdot (- \cos (u_{1})) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.81

$\frac{1}{2}$ और $- 1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot \frac{1}{2} \cos (u_{1}) (\frac{1}{2} \cdot (- \cos (u_{1})))) d u_{1}$

चरण 5.2.82

$\frac{1}{2}$ और $- 1$ को पुन: क्रमित करें.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot \frac{1}{2} \cos (u_{1}))) d u_{1}$

चरण 5.2.83

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot \frac{1}{2}) \cos (u_{1})) d u_{1}$

चरण 5.2.84

$\cos (u_{1})$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot \frac{1}{2} \cdot - 1 \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1})) d u_{1}$

चरण 5.2.85

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1})) d u_{1}$

चरण 5.2.86

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2}) \cos (u_{1}) d u_{1}$

चरण 5.2.87

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot - 1 \frac{1}{2} \cos (u_{1})) \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.88

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot - 1 \frac{1}{2}) \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.89

कोष्ठक ले जाएँ.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cos (u_{1}) (- 1 \cdot - 1) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.90

$\cos (u_{1})$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot \frac{1}{2} \cdot - 1 \cdot - 1 \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.91

$\frac{1}{2}$ ले जाएं.

$\frac{1}{2} \int 1 \cdot 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.92

$1$ को $1$ से गुणा करें.

$\frac{1}{2} \int 1 \cdot 1 \frac{1}{2} \frac{1}{2} \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.93

$1$ को $1$ से गुणा करें.

$\frac{1}{2} \int 1 (\frac{1}{2}) \frac{1}{2} \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.94

$\frac{1}{2}$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{2} \cdot \frac{1}{2} \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.95

$\frac{1}{2}$ को $\frac{1}{2}$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{2 \cdot 2} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.96

$2$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{4} \cdot \frac{1}{2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.97

$\frac{1}{4}$ को $\frac{1}{2}$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{4 \cdot 2} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.98

$4$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + 1 \cdot 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.99

$1$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.100

$- 1$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{1}{2} \cdot \frac{1}{2} \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.101

$- \frac{1}{2}$ और $\frac{1}{2}$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} - \frac{1}{2 \cdot 2} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.102

$2$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{1}{4} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.103

$- \frac{1}{4}$ और $\frac{1}{2}$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} - \frac{1}{4 \cdot 2} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.104

$4$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{1}{8} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.105

$\frac{1}{8}$ और $\cos (u_{1})$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.106

$- 1$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.107

$- 1$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.108

$- \frac{1}{2}$ और $\frac{1}{2}$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{1}{2 \cdot 2} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.109

$2$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{1}{4} \cos (u_{1}) \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.110

$\frac{1}{4}$ और $\cos (u_{1})$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{4} \cdot \frac{1}{2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.111

$- \frac{\cos (u_{1})}{4}$ और $\frac{1}{2}$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{4 \cdot 2} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.112

$4$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + 1 \cdot - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.113

$- 1$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} - 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.114

$- 1$ को $- 1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + 1 (\frac{1}{2}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.115

$\frac{1}{2}$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.116

$\frac{1}{2}$ को $\frac{1}{2}$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{1}{2 \cdot 2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.117

$2$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.118

$\frac{1}{4}$ और $\cos (u_{1})$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos (u_{1})}{4} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.119

$\frac{\cos (u_{1})}{4}$ को $\frac{1}{2}$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos (u_{1})}{4 \cdot 2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.120

$4$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos (u_{1})}{8} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.121

$\frac{\cos (u_{1})}{8}$ और $\cos (u_{1})$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos (u_{1}) \cos (u_{1})}{8} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.122

$\cos (u_{1})$ को $1$ के घात तक बढ़ाएं.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{1} (u_{1}) \cos (u_{1})}{8} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.123

$\cos (u_{1})$ को $1$ के घात तक बढ़ाएं.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{1} (u_{1}) \cos^{1} (u_{1})}{8} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.124

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{{\cos (u_{1})}^{1 + 1}}{8} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.125

$1$ और $1$ जोड़ें.

$\frac{1}{2} \int \frac{1}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.126

$- \frac{\cos (u_{1})}{8}$ में से $\frac{\cos (u_{1})}{8}$ घटाएं.

$\frac{1}{2} \int \frac{1}{8} - 2 \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.127

$- 2$ और $\frac{\cos (u_{1})}{8}$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.128

$- 1$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.129

$- 1$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.130

$\frac{1}{2}$ और $\cos (u_{1})$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{2} \cdot \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.131

$- \frac{\cos (u_{1})}{2}$ और $\frac{1}{2}$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{2 \cdot 2} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.132

$2$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{4} \cdot \frac{1}{2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.133

$- \frac{\cos (u_{1})}{4}$ और $\frac{1}{2}$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{4 \cdot 2} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.134

$4$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} - 1 \cdot 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.135

$- 1$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.136

$- 1$ को $- 1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + 1 (\frac{1}{2}) \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.137

$\frac{1}{2}$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.138

$\frac{1}{2}$ और $\cos (u_{1})$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos (u_{1})}{2} \cdot \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.139

$\frac{\cos (u_{1})}{2}$ को $\frac{1}{2}$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos (u_{1})}{2 \cdot 2} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.140

$2$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos (u_{1})}{4} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.141

$\frac{\cos (u_{1})}{4}$ को $\frac{1}{2}$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos (u_{1})}{4 \cdot 2} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.142

$4$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos (u_{1})}{8} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.143

$\frac{\cos (u_{1})}{8}$ और $\cos (u_{1})$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos (u_{1}) \cos (u_{1})}{8} - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.144

$\cos (u_{1})$ को $1$ के घात तक बढ़ाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{1} (u_{1}) \cos (u_{1})}{8} - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.145

$\cos (u_{1})$ को $1$ के घात तक बढ़ाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{1} (u_{1}) \cos^{1} (u_{1})}{8} - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.146

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{{\cos (u_{1})}^{1 + 1}}{8} - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.147

$1$ और $1$ जोड़ें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.148

$- 1$ को $- 1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.149

$1$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + 1 (\frac{1}{2}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.150

$\frac{1}{2}$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.151

$\frac{1}{2}$ और $\cos (u_{1})$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos (u_{1})}{2} \cdot \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.152

$\frac{\cos (u_{1})}{2}$ को $\frac{1}{2}$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos (u_{1})}{2 \cdot 2} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.153

$2$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos (u_{1})}{4} \cos (u_{1}) \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.154

$\frac{\cos (u_{1})}{4}$ और $\cos (u_{1})$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos (u_{1}) \cos (u_{1})}{4} \cdot \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.155

$\cos (u_{1})$ को $1$ के घात तक बढ़ाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{1} (u_{1}) \cos (u_{1})}{4} \cdot \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.156

$\cos (u_{1})$ को $1$ के घात तक बढ़ाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{1} (u_{1}) \cos^{1} (u_{1})}{4} \cdot \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.157

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{{\cos (u_{1})}^{1 + 1}}{4} \cdot \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.158

$1$ और $1$ जोड़ें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{4} \cdot \frac{1}{2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.159

$\frac{\cos^{2} (u_{1})}{4}$ को $\frac{1}{2}$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{4 \cdot 2} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.160

$4$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - 1 \cdot - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.161

$- 1$ को $- 1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.162

$- 1$ को $1$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.163

$\frac{1}{2}$ और $\cos (u_{1})$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{2} \cdot \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.164

$- \frac{\cos (u_{1})}{2}$ और $\frac{1}{2}$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{2 \cdot 2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.165

$2$ को $2$ से गुणा करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.166

$\frac{\cos (u_{1})}{4}$ और $\cos (u_{1})$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1}) \cos (u_{1})}{4} \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.167

$\cos (u_{1})$ को $1$ के घात तक बढ़ाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos^{1} (u_{1}) \cos (u_{1})}{4} \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.168

$\cos (u_{1})$ को $1$ के घात तक बढ़ाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos^{1} (u_{1}) \cos^{1} (u_{1})}{4} \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.169

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{{\cos (u_{1})}^{1 + 1}}{4} \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.170

$1$ और $1$ जोड़ें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos^{2} (u_{1})}{4} \cdot \frac{1}{2} \cos (u_{1}) d u_{1}$

चरण 5.2.171

$- \frac{\cos^{2} (u_{1})}{4}$ और $\frac{1}{2}$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos^{2} (u_{1})}{4 \cdot 2} \cos (u_{1}) d u_{1}$

चरण 5.2.172

$4$ को $2$ से गुणा करें.

चरण 5.2.173

$\frac{\cos^{2} (u_{1})}{8}$ और $\cos (u_{1})$ को मिलाएं.

चरण 5.2.174

$\cos (u_{1})$ को $1$ के घात तक बढ़ाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos^{2} (u_{1}) \cos^{1} (u_{1})}{8} d u_{1}$

चरण 5.2.175

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

चरण 5.2.176

$2$ और $1$ जोड़ें.

चरण 5.2.177

$\frac{\cos^{2} (u_{1})}{8}$ और $\frac{\cos^{2} (u_{1})}{8}$ जोड़ें.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + 2 \frac{\cos^{2} (u_{1})}{8} - \frac{\cos^{3} (u_{1})}{8} d u_{1}$

चरण 5.2.178

$2$ और $\frac{\cos^{2} (u_{1})}{8}$ को मिलाएं.

$\frac{1}{2} \int \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{2 \cos^{2} (u_{1})}{8} - \frac{\cos^{3} (u_{1})}{8} d u_{1}$

चरण 5.2.179

$\frac{- 2 \cos (u_{1})}{8}$ और $\frac{\cos^{2} (u_{1})}{8}$ को पुन: क्रमित करें.

$\frac{1}{2} \int \frac{1}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{- 2 \cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{2 \cos^{2} (u_{1})}{8} - \frac{\cos^{3} (u_{1})}{8} d u_{1}$

चरण 5.2.180

$\frac{1}{8}$ और $\frac{\cos^{2} (u_{1})}{8}$ को पुन: क्रमित करें.

$\frac{1}{2} \int \frac{\cos^{2} (u_{1})}{8} + \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} + \frac{2 \cos^{2} (u_{1})}{8} - \frac{\cos^{3} (u_{1})}{8} d u_{1}$

चरण 5.2.181

$\frac{2 \cos^{2} (u_{1})}{8}$ और $- \frac{\cos^{3} (u_{1})}{8}$ को पुन: क्रमित करें.

$\frac{1}{2} \int \frac{\cos^{2} (u_{1})}{8} + \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} - \frac{\cos^{3} (u_{1})}{8} + \frac{2 \cos^{2} (u_{1})}{8} d u_{1}$

चरण 5.2.182

$- \frac{\cos (u_{1})}{8}$ ले जाएं.

$\frac{1}{2} \int \frac{\cos^{2} (u_{1})}{8} + \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} - \frac{\cos^{3} (u_{1})}{8} + \frac{2 \cos^{2} (u_{1})}{8} - \frac{\cos (u_{1})}{8} d u_{1}$

चरण 5.2.183

$\frac{- 2 \cos (u_{1})}{8}$ ले जाएं.

$\frac{1}{2} \int \frac{\cos^{2} (u_{1})}{8} + \frac{1}{8} - \frac{\cos^{3} (u_{1})}{8} + \frac{2 \cos^{2} (u_{1})}{8} + \frac{- 2 \cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} d u_{1}$

चरण 5.2.184

$\frac{1}{8}$ ले जाएं.

$\frac{1}{2} \int \frac{\cos^{2} (u_{1})}{8} - \frac{\cos^{3} (u_{1})}{8} + \frac{2 \cos^{2} (u_{1})}{8} + \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} d u_{1}$

चरण 5.2.185

$\frac{\cos^{2} (u_{1})}{8}$ और $- \frac{\cos^{3} (u_{1})}{8}$ को पुन: क्रमित करें.

$\frac{1}{2} \int - \frac{\cos^{3} (u_{1})}{8} + \frac{\cos^{2} (u_{1})}{8} + \frac{2 \cos^{2} (u_{1})}{8} + \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} d u_{1}$

चरण 5.2.186

सामान्य भाजक पर न्यूमेरेटरों को जोड़ें.

$\frac{1}{2} \int - \frac{\cos^{3} (u_{1})}{8} + \frac{\cos^{2} (u_{1}) + 2 \cos^{2} (u_{1})}{8} + \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} d u_{1}$

चरण 5.2.187

$\cos^{2} (u_{1})$ और $2 \cos^{2} (u_{1})$ जोड़ें.

$\frac{1}{2} \int - \frac{\cos^{3} (u_{1})}{8} + \frac{3 \cos^{2} (u_{1})}{8} + \frac{1}{8} + \frac{- 2 \cos (u_{1})}{8} - \frac{\cos (u_{1})}{8} d u_{1}$

चरण 5.2.188

सामान्य भाजक पर न्यूमेरेटरों को जोड़ें.

$\frac{1}{2} \int - \frac{\cos^{3} (u_{1})}{8} + \frac{3 \cos^{2} (u_{1})}{8} + \frac{1}{8} + \frac{- 2 \cos (u_{1}) - \cos (u_{1})}{8} d u_{1}$

चरण 5.2.189

$- 2 \cos (u_{1})$ में से $\cos (u_{1})$ घटाएं.

$\frac{1}{2} \int - \frac{\cos^{3} (u_{1})}{8} + \frac{3 \cos^{2} (u_{1})}{8} + \frac{1}{8} + \frac{- 3 \cos (u_{1})}{8} d u_{1}$

चरण 5.3

भिन्न के सामने ऋणात्मक ले जाएँ.

$\frac{1}{2} \int - \frac{\cos^{3} (u_{1})}{8} + \frac{3 \cos^{2} (u_{1})}{8} + \frac{1}{8} - \frac{3 \cos (u_{1})}{8} d u_{1}$

चरण 6

एकल समाकलन को कई समाकलन में विभाजित करें.

$\frac{1}{2} (\int - \frac{\cos^{3} (u_{1})}{8} d u_{1} + \int \frac{3 \cos^{2} (u_{1})}{8} d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 7

चूँकि $- 1$ बटे $u_{1}$ अचर है, $- 1$ को समाकलन से हटा दें.

$\frac{1}{2} (- \int \frac{\cos^{3} (u_{1})}{8} d u_{1} + \int \frac{3 \cos^{2} (u_{1})}{8} d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 8

चूँकि $\frac{1}{8}$ बटे $u_{1}$ अचर है, $\frac{1}{8}$ को समाकलन से हटा दें.

$\frac{1}{2} (- (\frac{1}{8} \int \cos^{3} (u_{1}) d u_{1}) + \int \frac{3 \cos^{2} (u_{1})}{8} d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 9

$\cos^{2} (u_{1})$ का गुणनखंड करें.

$\frac{1}{2} (- \frac{1}{8} \int \cos^{2} (u_{1}) \cos (u_{1}) d u_{1} + \int \frac{3 \cos^{2} (u_{1})}{8} d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 10

पाइथागोरस पहचान का उपयोग करते हुए, $\cos^{2} (u_{1})$ को $1 - \sin^{2} (u_{1})$ के रूप में फिर से लिखें.

$\frac{1}{2} (- \frac{1}{8} \int (1 - \sin^{2} (u_{1})) \cos (u_{1}) d u_{1} + \int \frac{3 \cos^{2} (u_{1})}{8} d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 11

मान लीजिए $u_{2} = \sin (u_{1})$ .फिर $d u_{2} = \cos (u_{1}) d u_{1}$ , तो $\frac{1}{\cos (u_{1})} d u_{2} = d u_{1}$ . $u_{2}$ और $d$ $u_{2}$ का उपयोग करके फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 11.1

मान लें $u_{2} = \sin (u_{1})$ . $\frac{d u_{2}}{d u_{1}}$ ज्ञात करें.

और स्टेप्स के लिए टैप करें…

चरण 11.1.1

$\sin (u_{1})$ को अवकलित करें.

$\frac{d}{d u_{1}} [\sin (u_{1})]$

चरण 11.1.2

$u_{1}$ के संबंध में $\sin (u_{1})$ का व्युत्पन्न $\cos (u_{1})$ है.

$\cos (u_{1})$

चरण 11.2

$u_{2}$ और $d u_{2}$ का उपयोग करके समस्या को फिर से लिखें.

$\frac{1}{2} (- \frac{1}{8} \int 1 - {u_{2}}^{2} d u_{2} + \int \frac{3 \cos^{2} (u_{1})}{8} d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 12

एकल समाकलन को कई समाकलन में विभाजित करें.

$\frac{1}{2} (- \frac{1}{8} (\int d u_{2} + \int - {u_{2}}^{2} d u_{2}) + \int \frac{3 \cos^{2} (u_{1})}{8} d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 13

स्थिरांक नियम लागू करें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C + \int - {u_{2}}^{2} d u_{2}) + \int \frac{3 \cos^{2} (u_{1})}{8} d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 14

चूँकि $- 1$ बटे $u_{2}$ अचर है, $- 1$ को समाकलन से हटा दें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - \int {u_{2}}^{2} d u_{2}) + \int \frac{3 \cos^{2} (u_{1})}{8} d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 15

घात नियम के अनुसार, $u_{2}$ के संबंध में ${u_{2}}^{2}$ का समाकलन $\frac{1}{3} {u_{2}}^{3}$ है.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{1}{3} {u_{2}}^{3} + C)) + \int \frac{3 \cos^{2} (u_{1})}{8} d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 16

$\frac{1}{3}$ और ${u_{2}}^{3}$ को मिलाएं.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \int \frac{3 \cos^{2} (u_{1})}{8} d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 17

चूँकि $\frac{3}{8}$ बटे $u_{1}$ अचर है, $\frac{3}{8}$ को समाकलन से हटा दें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{8} \int \cos^{2} (u_{1}) d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 18

$\cos^{2} (u_{1})$ को $\frac{1 + \cos (2 u_{1})}{2}$ के रूप में फिर से लिखने के लिए अर्ध-कोण सूत्र का प्रयोग करें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{8} \int \frac{1 + \cos (2 u_{1})}{2} d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 19

चूँकि $\frac{1}{2}$ बटे $u_{1}$ अचर है, $\frac{1}{2}$ को समाकलन से हटा दें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{8} (\frac{1}{2} \int 1 + \cos (2 u_{1}) d u_{1}) + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 20

सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 20.1

$\frac{1}{2}$ को $\frac{3}{8}$ से गुणा करें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{2 \cdot 8} \int 1 + \cos (2 u_{1}) d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 20.2

$2$ को $8$ से गुणा करें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{16} \int 1 + \cos (2 u_{1}) d u_{1} + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 21

एकल समाकलन को कई समाकलन में विभाजित करें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{16} (\int d u_{1} + \int \cos (2 u_{1}) d u_{1}) + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 22

स्थिरांक नियम लागू करें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{16} (u_{1} + C + \int \cos (2 u_{1}) d u_{1}) + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 23

मान लीजिए $u_{3} = 2 u_{1}$ .फिर $d u_{3} = 2 d u_{1}$ , तो $\frac{1}{2} d u_{3} = d u_{1}$ . $u_{3}$ और $d$ $u_{3}$ का उपयोग करके फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 23.1

मान लें $u_{3} = 2 u_{1}$ . $\frac{d u_{3}}{d u_{1}}$ ज्ञात करें.

और स्टेप्स के लिए टैप करें…

चरण 23.1.1

$2 u_{1}$ को अवकलित करें.

$\frac{d}{d u_{1}} [2 u_{1}]$

चरण 23.1.2

चूंकि $2$ , $u_{1}$ के संबंध में स्थिर है, $u_{1}$ के संबंध में $2 u_{1}$ का व्युत्पन्न $2 \frac{d}{d u_{1}} [u_{1}]$ है.

$2 \frac{d}{d u_{1}} [u_{1}]$

चरण 23.1.3

घात नियम का उपयोग करके अवकलन करें, जिसमें यह वर्णन हो कि $\frac{d}{d u_{1}} [{u_{1}}^{n}]$ $n {u_{1}}^{n - 1}$ है, जहाँ $n = 1$ है.

$2 \cdot 1$

चरण 23.1.4

$2$ को $1$ से गुणा करें.

$2$

चरण 23.2

$u_{3}$ और $d u_{3}$ का उपयोग करके समस्या को फिर से लिखें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{16} (u_{1} + C + \int \cos (u_{3}) \frac{1}{2} d u_{3}) + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 24

$\cos (u_{3})$ और $\frac{1}{2}$ को मिलाएं.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{16} (u_{1} + C + \int \frac{\cos (u_{3})}{2} d u_{3}) + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 25

चूँकि $\frac{1}{2}$ बटे $u_{3}$ अचर है, $\frac{1}{2}$ को समाकलन से हटा दें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{16} (u_{1} + C + \frac{1}{2} \int \cos (u_{3}) d u_{3}) + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 26

$u_{3}$ के संबंध में $\cos (u_{3})$ का इंटीग्रल $\sin (u_{3})$ है.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{16} (u_{1} + C + \frac{1}{2} (\sin (u_{3}) + C)) + \int \frac{1}{8} d u_{1} + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 27

स्थिरांक नियम लागू करें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{16} (u_{1} + C + \frac{1}{2} (\sin (u_{3}) + C)) + \frac{1}{8} u_{1} + C + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 28

$\frac{1}{8}$ और $u_{1}$ को मिलाएं.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{16} (u_{1} + C + \frac{1}{2} (\sin (u_{3}) + C)) + \frac{u_{1}}{8} + C + \int - \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 29

चूँकि $- 1$ बटे $u_{1}$ अचर है, $- 1$ को समाकलन से हटा दें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{16} (u_{1} + C + \frac{1}{2} (\sin (u_{3}) + C)) + \frac{u_{1}}{8} + C - \int \frac{3 \cos (u_{1})}{8} d u_{1})$

चरण 30

चूँकि $\frac{3}{8}$ बटे $u_{1}$ अचर है, $\frac{3}{8}$ को समाकलन से हटा दें.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{16} (u_{1} + C + \frac{1}{2} (\sin (u_{3}) + C)) + \frac{u_{1}}{8} + C - (\frac{3}{8} \int \cos (u_{1}) d u_{1}))$

चरण 31

$u_{1}$ के संबंध में $\cos (u_{1})$ का इंटीग्रल $\sin (u_{1})$ है.

$\frac{1}{2} (- \frac{1}{8} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) + \frac{3}{16} (u_{1} + C + \frac{1}{2} (\sin (u_{3}) + C)) + \frac{u_{1}}{8} + C - \frac{3}{8} (\sin (u_{1}) + C))$

चरण 32

सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 32.1

सरल करें.

$\frac{1}{2} (- \frac{u_{2}}{8} + \frac{{u_{2}}^{3}}{24} + \frac{3 u_{1}}{16} + \frac{3 \sin (u_{3})}{32} + \frac{u_{1}}{8} - \frac{3 \sin (u_{1})}{8}) + C$

चरण 32.2

सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 32.2.1

$\frac{u_{1}}{8}$ को एक सामान्य भाजक वाली भिन्न के रूप में लिखने के लिए, $\frac{2}{2}$ से गुणा करें.

$\frac{1}{2} (- \frac{u_{2}}{8} + \frac{{u_{2}}^{3}}{24} + \frac{3 u_{1}}{16} + \frac{u_{1}}{8} \cdot \frac{2}{2} + \frac{3 \sin (u_{3})}{32} - \frac{3 \sin (u_{1})}{8}) + C$

चरण 32.2.2

प्रत्येक व्यंजक को $16$ के सामान्य भाजक के साथ लिखें, प्रत्येक को $1$ के उपयुक्त गुणनखंड से गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 32.2.2.1

$\frac{u_{1}}{8}$ को $\frac{2}{2}$ से गुणा करें.

$\frac{1}{2} (- \frac{u_{2}}{8} + \frac{{u_{2}}^{3}}{24} + \frac{3 u_{1}}{16} + \frac{u_{1} \cdot 2}{8 \cdot 2} + \frac{3 \sin (u_{3})}{32} - \frac{3 \sin (u_{1})}{8}) + C$

चरण 32.2.2.2

$8$ को $2$ से गुणा करें.

$\frac{1}{2} (- \frac{u_{2}}{8} + \frac{{u_{2}}^{3}}{24} + \frac{3 u_{1}}{16} + \frac{u_{1} \cdot 2}{16} + \frac{3 \sin (u_{3})}{32} - \frac{3 \sin (u_{1})}{8}) + C$

चरण 32.2.3

सामान्य भाजक पर न्यूमेरेटरों को जोड़ें.

$\frac{1}{2} (- \frac{u_{2}}{8} + \frac{{u_{2}}^{3}}{24} + \frac{3 u_{1} + u_{1} \cdot 2}{16} + \frac{3 \sin (u_{3})}{32} - \frac{3 \sin (u_{1})}{8}) + C$

चरण 32.2.4

$2$ को $u_{1}$ के बाईं ओर ले जाएं.

$\frac{1}{2} (- \frac{u_{2}}{8} + \frac{{u_{2}}^{3}}{24} + \frac{3 u_{1} + 2 \cdot u_{1}}{16} + \frac{3 \sin (u_{3})}{32} - \frac{3 \sin (u_{1})}{8}) + C$

चरण 32.2.5

$3 u_{1}$ और $2 u_{1}$ जोड़ें.

$\frac{1}{2} (- \frac{u_{2}}{8} + \frac{{u_{2}}^{3}}{24} + \frac{5 u_{1}}{16} + \frac{3 \sin (u_{3})}{32} - \frac{3 \sin (u_{1})}{8}) + C$

चरण 33

प्रत्येक एकीकरण प्रतिस्थापन चर के लिए वापस प्रतिस्थापित करें.

और स्टेप्स के लिए टैप करें…

चरण 33.1

$u_{2}$ की सभी घटनाओं को $\sin (u_{1})$ से बदलें.

$\frac{1}{2} (- \frac{\sin (u_{1})}{8} + \frac{\sin^{3} (u_{1})}{24} + \frac{5 u_{1}}{16} + \frac{3 \sin (u_{3})}{32} - \frac{3 \sin (u_{1})}{8}) + C$

चरण 33.2

$u_{1}$ की सभी घटनाओं को $2 x$ से बदलें.

$\frac{1}{2} (- \frac{\sin (2 x)}{8} + \frac{\sin^{3} (2 x)}{24} + \frac{5 (2 x)}{16} + \frac{3 \sin (u_{3})}{32} - \frac{3 \sin (2 x)}{8}) + C$

चरण 33.3

$u_{3}$ की सभी घटनाओं को $2 u_{1}$ से बदलें.

$\frac{1}{2} (- \frac{\sin (2 x)}{8} + \frac{\sin^{3} (2 x)}{24} + \frac{5 (2 x)}{16} + \frac{3 \sin (2 u_{1})}{32} - \frac{3 \sin (2 x)}{8}) + C$

चरण 33.4

$u_{1}$ की सभी घटनाओं को $2 x$ से बदलें.

$\frac{1}{2} (- \frac{\sin (2 x)}{8} + \frac{\sin^{3} (2 x)}{24} + \frac{5 (2 x)}{16} + \frac{3 \sin (2 (2 x))}{32} - \frac{3 \sin (2 x)}{8}) + C$

चरण 34

सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 34.1

सामान्य भाजक पर न्यूमेरेटरों को जोड़ें.

$\frac{1}{2} (\frac{- \sin (2 x) - 3 \sin (2 x)}{8} + \frac{\sin^{3} (2 x)}{24} + \frac{5 (2 x)}{16} + \frac{3 \sin (2 (2 x))}{32}) + C$

चरण 34.2

$- \sin (2 x)$ में से $3 \sin (2 x)$ घटाएं.

$\frac{1}{2} (\frac{- 4 \sin (2 x)}{8} + \frac{\sin^{3} (2 x)}{24} + \frac{5 (2 x)}{16} + \frac{3 \sin (2 (2 x))}{32}) + C$

चरण 34.3

प्रत्येक पद को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 34.3.1

$- 4$ और $8$ के उभयनिष्ठ गुणनखंड को रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 34.3.1.1

$- 4 \sin (2 x)$ में से $4$ का गुणनखंड करें.

$\frac{1}{2} (\frac{4 (- \sin (2 x))}{8} + \frac{\sin^{3} (2 x)}{24} + \frac{5 (2 x)}{16} + \frac{3 \sin (2 (2 x))}{32}) + C$

चरण 34.3.1.2

उभयनिष्ठ गुणनखंडों को रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 34.3.1.2.1

$8$ में से $4$ का गुणनखंड करें.

$\frac{1}{2} (\frac{4 (- \sin (2 x))}{4 (2)} + \frac{\sin^{3} (2 x)}{24} + \frac{5 (2 x)}{16} + \frac{3 \sin (2 (2 x))}{32}) + C$

चरण 34.3.1.2.2

उभयनिष्ठ गुणनखंड रद्द करें.

$\frac{1}{2} (\frac{4 (- \sin (2 x))}{4 \cdot 2} + \frac{\sin^{3} (2 x)}{24} + \frac{5 (2 x)}{16} + \frac{3 \sin (2 (2 x))}{32}) + C$

चरण 34.3.1.2.3

व्यंजक को फिर से लिखें.

$\frac{1}{2} (\frac{- \sin (2 x)}{2} + \frac{\sin^{3} (2 x)}{24} + \frac{5 (2 x)}{16} + \frac{3 \sin (2 (2 x))}{32}) + C$

चरण 34.3.2

भिन्न के सामने ऋणात्मक ले जाएँ.

$\frac{1}{2} (- \frac{\sin (2 x)}{2} + \frac{\sin^{3} (2 x)}{24} + \frac{5 (2 x)}{16} + \frac{3 \sin (2 (2 x))}{32}) + C$

चरण 34.3.3

$2$ और $16$ के उभयनिष्ठ गुणनखंड को रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 34.3.3.1

$5 (2 x)$ में से $2$ का गुणनखंड करें.

$\frac{1}{2} (- \frac{\sin (2 x)}{2} + \frac{\sin^{3} (2 x)}{24} + \frac{2 (5 (x))}{16} + \frac{3 \sin (2 (2 x))}{32}) + C$

चरण 34.3.3.2

उभयनिष्ठ गुणनखंडों को रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 34.3.3.2.1

$16$ में से $2$ का गुणनखंड करें.

$\frac{1}{2} (- \frac{\sin (2 x)}{2} + \frac{\sin^{3} (2 x)}{24} + \frac{2 (5 (x))}{2 \cdot 8} + \frac{3 \sin (2 (2 x))}{32}) + C$

चरण 34.3.3.2.2

उभयनिष्ठ गुणनखंड रद्द करें.

$\frac{1}{2} (- \frac{\sin (2 x)}{2} + \frac{\sin^{3} (2 x)}{24} + \frac{2 (5 (x))}{2 \cdot 8} + \frac{3 \sin (2 (2 x))}{32}) + C$

चरण 34.3.3.2.3

व्यंजक को फिर से लिखें.

$\frac{1}{2} (- \frac{\sin (2 x)}{2} + \frac{\sin^{3} (2 x)}{24} + \frac{5 (x)}{8} + \frac{3 \sin (2 (2 x))}{32}) + C$

चरण 34.3.4

$2$ को $2$ से गुणा करें.

$\frac{1}{2} (- \frac{\sin (2 x)}{2} + \frac{\sin^{3} (2 x)}{24} + \frac{5 x}{8} + \frac{3 \sin (4 x)}{32}) + C$

चरण 34.4

वितरण गुणधर्म लागू करें.

$\frac{1}{2} (- \frac{\sin (2 x)}{2}) + \frac{1}{2} \cdot \frac{\sin^{3} (2 x)}{24} + \frac{1}{2} \cdot \frac{5 x}{8} + \frac{1}{2} \cdot \frac{3 \sin (4 x)}{32} + C$

चरण 34.5

सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 34.5.1

$\frac{1}{2} (- \frac{\sin (2 x)}{2})$ गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 34.5.1.1

$\frac{1}{2}$ को $\frac{\sin (2 x)}{2}$ से गुणा करें.

$- \frac{\sin (2 x)}{2 \cdot 2} + \frac{1}{2} \cdot \frac{\sin^{3} (2 x)}{24} + \frac{1}{2} \cdot \frac{5 x}{8} + \frac{1}{2} \cdot \frac{3 \sin (4 x)}{32} + C$

चरण 34.5.1.2

$2$ को $2$ से गुणा करें.

$- \frac{\sin (2 x)}{4} + \frac{1}{2} \cdot \frac{\sin^{3} (2 x)}{24} + \frac{1}{2} \cdot \frac{5 x}{8} + \frac{1}{2} \cdot \frac{3 \sin (4 x)}{32} + C$

चरण 34.5.2

जोड़ना.

$- \frac{\sin (2 x)}{4} + \frac{1 \sin^{3} (2 x)}{2 \cdot 24} + \frac{1}{2} \cdot \frac{5 x}{8} + \frac{1}{2} \cdot \frac{3 \sin (4 x)}{32} + C$

चरण 34.5.3

$\frac{1}{2} \cdot \frac{5 x}{8}$ गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 34.5.3.1

$\frac{1}{2}$ को $\frac{5 x}{8}$ से गुणा करें.

$- \frac{\sin (2 x)}{4} + \frac{1 \sin^{3} (2 x)}{2 \cdot 24} + \frac{5 x}{2 \cdot 8} + \frac{1}{2} \cdot \frac{3 \sin (4 x)}{32} + C$

चरण 34.5.3.2

$2$ को $8$ से गुणा करें.

$- \frac{\sin (2 x)}{4} + \frac{1 \sin^{3} (2 x)}{2 \cdot 24} + \frac{5 x}{16} + \frac{1}{2} \cdot \frac{3 \sin (4 x)}{32} + C$

चरण 34.5.4

$\frac{1}{2} \cdot \frac{3 \sin (4 x)}{32}$ गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 34.5.4.1

$\frac{1}{2}$ को $\frac{3 \sin (4 x)}{32}$ से गुणा करें.

$- \frac{\sin (2 x)}{4} + \frac{1 \sin^{3} (2 x)}{2 \cdot 24} + \frac{5 x}{16} + \frac{3 \sin (4 x)}{2 \cdot 32} + C$

चरण 34.5.4.2

$2$ को $32$ से गुणा करें.

$- \frac{\sin (2 x)}{4} + \frac{1 \sin^{3} (2 x)}{2 \cdot 24} + \frac{5 x}{16} + \frac{3 \sin (4 x)}{64} + C$

चरण 34.6

प्रत्येक पद को सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 34.6.1

$\sin^{3} (2 x)$ को $1$ से गुणा करें.

$- \frac{\sin (2 x)}{4} + \frac{\sin^{3} (2 x)}{2 \cdot 24} + \frac{5 x}{16} + \frac{3 \sin (4 x)}{64} + C$

चरण 34.6.2

$2$ को $24$ से गुणा करें.

$- \frac{\sin (2 x)}{4} + \frac{\sin^{3} (2 x)}{48} + \frac{5 x}{16} + \frac{3 \sin (4 x)}{64} + C$

चरण 35

पदों को पुन: व्यवस्थित करें

$- \frac{1}{4} \sin (2 x) + \frac{1}{48} \sin^{3} (2 x) + \frac{5}{16} x + \frac{3}{64} \sin (4 x) + C$