कैलकुलस उदाहरण

$\int \sin^{4} (x) \cos^{2} (x) d x$

चरण 1

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

$\int \sin^{4} (x) \frac{1 + \cos (2 x)}{2} d x$

चरण 2

गुणनखंड निकालकर सरलीकृत करें.

और स्टेप्स के लिए टैप करें…

चरण 2.1

$4$ में से $2$ का गुणनखंड करें.

$\int {\sin (x)}^{2 (2)} \frac{1 + \cos (2 x)}{2} d x$

चरण 2.2

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

$\int {(\sin^{2} (x))}^{2} \frac{1 + \cos (2 x)}{2} d x$

चरण 3

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

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

चरण 4

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 4.1

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

और स्टेप्स के लिए टैप करें…

चरण 4.1.1

$2 x$ को अवकलित करें.

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

चरण 4.1.2

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 4.1.3

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 4.1.4

$2$ को $1$ से गुणा करें.

$2$

चरण 4.2

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

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

चरण 5

से गुणा करके सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.1

सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.1.1

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

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

चरण 5.1.2

$2$ को $2$ से गुणा करें.

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

चरण 5.2

विनिमय के साथ सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 5.2.1

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

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

चरण 5.2.2

एक गुणनफल के रूप में $\frac{1 + \cos (u_{1})}{4}$ को फिर से लिखें.

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

चरण 5.3

${(\frac{1}{2} \cdot (1 - \cos (u_{1})))}^{2} (\frac{1}{4} \cdot (1 + \cos (u_{1})))$ का प्रसार करें.

और स्टेप्स के लिए टैप करें…

चरण 5.3.1

एक गुणनफल के रूप में घातांक को फिर से लिखें.

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

चरण 5.3.2

वितरण गुणधर्म लागू करें.

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

चरण 5.3.3

वितरण गुणधर्म लागू करें.

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

चरण 5.3.4

वितरण गुणधर्म लागू करें.

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

चरण 5.3.5

वितरण गुणधर्म लागू करें.

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

चरण 5.3.6

वितरण गुणधर्म लागू करें.

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

चरण 5.3.7

वितरण गुणधर्म लागू करें.

चरण 5.3.8

वितरण गुणधर्म लागू करें.

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

चरण 5.3.9

वितरण गुणधर्म लागू करें.

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

चरण 5.3.10

वितरण गुणधर्म लागू करें.

चरण 5.3.11

वितरण गुणधर्म लागू करें.

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

चरण 5.3.12

वितरण गुणधर्म लागू करें.

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

चरण 5.3.13

वितरण गुणधर्म लागू करें.

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

चरण 5.3.14

वितरण गुणधर्म लागू करें.

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

चरण 5.3.15

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

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

चरण 5.3.16

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

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

चरण 5.3.17

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.18

$\frac{1}{4}$ और $1$ को पुन: क्रमित करें.

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

चरण 5.3.19

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.20

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.21

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

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

चरण 5.3.22

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

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

चरण 5.3.23

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.24

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

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

चरण 5.3.25

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

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

चरण 5.3.26

कोष्ठक ले जाएँ.

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

चरण 5.3.27

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.28

$\frac{1}{4}$ और $1$ को पुन: क्रमित करें.

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

चरण 5.3.29

$\cos (u_{1})$ ले जाएं.

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

चरण 5.3.30

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.31

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.32

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

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

चरण 5.3.33

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

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

चरण 5.3.34

कोष्ठक ले जाएँ.

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

चरण 5.3.35

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.36

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

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

चरण 5.3.37

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

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

चरण 5.3.38

$\cos (u_{1})$ ले जाएं.

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

चरण 5.3.39

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.40

$\frac{1}{4}$ और $1$ को पुन: क्रमित करें.

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

चरण 5.3.41

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.42

$\cos (u_{1})$ ले जाएं.

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

चरण 5.3.43

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.44

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

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

चरण 5.3.45

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

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

चरण 5.3.46

$\cos (u_{1})$ ले जाएं.

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

चरण 5.3.47

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.48

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

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

चरण 5.3.49

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

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

चरण 5.3.50

कोष्ठक ले जाएँ.

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

चरण 5.3.51

$\cos (u_{1})$ ले जाएं.

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

चरण 5.3.52

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.53

$\frac{1}{4}$ और $1$ को पुन: क्रमित करें.

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

चरण 5.3.54

$\cos (u_{1})$ ले जाएं.

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

चरण 5.3.55

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.56

$\cos (u_{1})$ ले जाएं.

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

चरण 5.3.57

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.58

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

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

चरण 5.3.59

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

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

चरण 5.3.60

कोष्ठक ले जाएँ.

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

चरण 5.3.61

$\cos (u_{1})$ ले जाएं.

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

चरण 5.3.62

$\frac{1}{2}$ ले जाएं.

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

चरण 5.3.63

$1$ को $1$ से गुणा करें.

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

चरण 5.3.64

$1$ को $1$ से गुणा करें.

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

चरण 5.3.65

$\frac{1}{2}$ को $1$ से गुणा करें.

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

चरण 5.3.66

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

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

चरण 5.3.67

$2$ को $2$ से गुणा करें.

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

चरण 5.3.68

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

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

चरण 5.3.69

$4$ को $4$ से गुणा करें.

$\int \frac{1}{16} + 1 \cdot 1 \frac{1}{2} \frac{1}{2} \frac{1}{4} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.70

$1$ को $1$ से गुणा करें.

$\int \frac{1}{16} + 1 (\frac{1}{2}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.71

$\frac{1}{2}$ को $1$ से गुणा करें.

$\int \frac{1}{16} + \frac{1}{2} \cdot \frac{1}{2} \frac{1}{4} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.72

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

$\int \frac{1}{16} + \frac{1}{2 \cdot 2} \cdot \frac{1}{4} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.73

$2$ को $2$ से गुणा करें.

$\int \frac{1}{16} + \frac{1}{4} \cdot \frac{1}{4} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.74

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

$\int \frac{1}{16} + \frac{1}{4 \cdot 4} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.75

$4$ को $4$ से गुणा करें.

$\int \frac{1}{16} + \frac{1}{16} \cos (u_{1}) + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.76

$\frac{1}{16}$ और $\cos (u_{1})$ को मिलाएं.

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} + 1 \cdot - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.77

$- 1$ को $1$ से गुणा करें.

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - 1 \cdot 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.78

$- 1$ को $1$ से गुणा करें.

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) \frac{1}{4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.79

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

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{1}{2 \cdot 2} \cos (u_{1}) \frac{1}{4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.80

$2$ को $2$ से गुणा करें.

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{1}{4} \cos (u_{1}) \frac{1}{4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.81

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

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{4} \cdot \frac{1}{4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.82

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

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{4 \cdot 4} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.83

$4$ को $4$ से गुणा करें.

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} + 1 \cdot - 1 \frac{1}{2} \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.84

$- 1$ को $1$ से गुणा करें.

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{1}{2} \cdot \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.85

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

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{1}{2 \cdot 2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.86

$2$ को $2$ से गुणा करें.

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{1}{4} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.87

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

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{4} \cdot \frac{1}{4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.88

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

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{4 \cdot 4} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.89

$4$ को $4$ से गुणा करें.

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.90

$\frac{\cos (u_{1})}{16}$ और $\cos (u_{1})$ को मिलाएं.

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1}) \cos (u_{1})}{16} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.91

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

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{1} (u_{1}) \cos (u_{1})}{16} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.92

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

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{1} (u_{1}) \cos^{1} (u_{1})}{16} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.93

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

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{{\cos (u_{1})}^{1 + 1}}{16} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.94

$1$ और $1$ जोड़ें.

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.95

$\frac{\cos (u_{1})}{16}$ में से $\frac{\cos (u_{1})}{16}$ घटाएं.

$\int \frac{1}{16} + 0 - \frac{\cos^{2} (u_{1})}{16} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.96

$0$ में से $\frac{\cos^{2} (u_{1})}{16}$ घटाएं.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - 1 \cdot 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.97

$- 1$ को $1$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.98

$- 1$ को $1$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.99

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{2} \cdot \frac{1}{2} \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.100

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{2 \cdot 2} \cdot \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.101

$2$ को $2$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{4} \cdot \frac{1}{4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.102

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{4 \cdot 4} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.103

$4$ को $4$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.104

$- 1$ को $1$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{1}{2} \cos (u_{1}) \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.105

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{2} \cdot \frac{1}{2} \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.106

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{2 \cdot 2} \cdot \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.107

$2$ को $2$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{4} \cdot \frac{1}{4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.108

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{4 \cdot 4} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.109

$4$ को $4$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} \cos (u_{1}) - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.110

$\frac{\cos (u_{1})}{16}$ और $\cos (u_{1})$ को मिलाएं.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1}) \cos (u_{1})}{16} - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.111

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{1} (u_{1}) \cos (u_{1})}{16} - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.112

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{1} (u_{1}) \cos^{1} (u_{1})}{16} - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.113

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{{\cos (u_{1})}^{1 + 1}}{16} - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.114

$1$ और $1$ जोड़ें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - 1 \cdot - 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.115

$- 1$ को $- 1$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + 1 \cdot 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.116

$1$ को $1$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + 1 (\frac{1}{2}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.117

$\frac{1}{2}$ को $1$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.118

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos (u_{1})}{2} \cdot \frac{1}{2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.119

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos (u_{1})}{2 \cdot 2} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.120

$2$ को $2$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos (u_{1})}{4} \cos (u_{1}) \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.121

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos (u_{1}) \cos (u_{1})}{4} \cdot \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.122

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{1} (u_{1}) \cos (u_{1})}{4} \cdot \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.123

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{1} (u_{1}) \cos^{1} (u_{1})}{4} \cdot \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.124

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{{\cos (u_{1})}^{1 + 1}}{4} \cdot \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.125

$1$ और $1$ जोड़ें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{4} \cdot \frac{1}{4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.126

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{4 \cdot 4} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.127

$4$ को $4$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - 1 \cdot - 1 \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.128

$- 1$ को $- 1$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} + 1 (\frac{1}{2}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.129

$\frac{1}{2}$ को $1$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} + \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.130

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} + \frac{\cos (u_{1})}{2} \cdot \frac{1}{2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.131

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} + \frac{\cos (u_{1})}{2 \cdot 2} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.132

$2$ को $2$ से गुणा करें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} + \frac{\cos (u_{1})}{4} \cos (u_{1}) \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.133

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} + \frac{\cos (u_{1}) \cos (u_{1})}{4} \cdot \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.134

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{1} (u_{1}) \cos (u_{1})}{4} \cdot \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.135

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{1} (u_{1}) \cos^{1} (u_{1})}{4} \cdot \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.136

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} + \frac{{\cos (u_{1})}^{1 + 1}}{4} \cdot \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.137

$1$ और $1$ जोड़ें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{4} \cdot \frac{1}{4} \cos (u_{1}) d u_{1}$

चरण 5.3.138

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

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{4 \cdot 4} \cos (u_{1}) d u_{1}$

चरण 5.3.139

$4$ को $4$ से गुणा करें.

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

चरण 5.3.140

$\frac{\cos^{2} (u_{1})}{16}$ और $\cos (u_{1})$ को मिलाएं.

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

चरण 5.3.141

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

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

चरण 5.3.142

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

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

चरण 5.3.143

$2$ और $1$ जोड़ें.

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

चरण 5.3.144

$- \frac{\cos^{2} (u_{1})}{16}$ और $\frac{\cos^{2} (u_{1})}{16}$ जोड़ें.

$\int \frac{1}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} + 0 + \frac{\cos^{3} (u_{1})}{16} d u_{1}$

चरण 5.3.145

$0$ और $\frac{\cos^{3} (u_{1})}{16}$ जोड़ें.

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

चरण 5.3.146

$\frac{1}{16}$ और $- \frac{\cos^{2} (u_{1})}{16}$ को पुन: क्रमित करें.

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

चरण 5.3.147

$- \frac{\cos (u_{1})}{16}$ और $\frac{\cos^{3} (u_{1})}{16}$ को पुन: क्रमित करें.

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

चरण 5.3.148

$\frac{1}{16}$ ले जाएं.

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

चरण 5.3.149

$- \frac{\cos^{2} (u_{1})}{16}$ और $\frac{\cos^{3} (u_{1})}{16}$ को पुन: क्रमित करें.

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

चरण 6

एकल समाकलन को कई समाकलन में विभाजित करें.

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

चरण 7

चूँकि $\frac{1}{16}$ बटे $u_{1}$ अचर है, $\frac{1}{16}$ को समाकलन से हटा दें.

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

चरण 8

$\cos^{2} (u_{1})$ का गुणनखंड करें.

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

चरण 9

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

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

चरण 10

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 10.1

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

और स्टेप्स के लिए टैप करें…

चरण 10.1.1

$\sin (u_{1})$ को अवकलित करें.

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

चरण 10.1.2

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

$\cos (u_{1})$

चरण 10.2

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

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

चरण 11

एकल समाकलन को कई समाकलन में विभाजित करें.

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

चरण 12

स्थिरांक नियम लागू करें.

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

चरण 13

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

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

चरण 14

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

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

चरण 15

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

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

चरण 16

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

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

चरण 17

चूँकि $\frac{1}{16}$ बटे $u_{1}$ अचर है, $\frac{1}{16}$ को समाकलन से हटा दें.

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

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.

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

चरण 19

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

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

चरण 20

सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 20.1

$\frac{1}{2}$ को $\frac{1}{16}$ से गुणा करें.

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

चरण 20.2

$2$ को $16$ से गुणा करें.

$\frac{1}{16} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) - \frac{1}{32} \int 1 + \cos (2 u_{1}) d u_{1} + \int \frac{1}{16} d u_{1} + \int - \frac{\cos (u_{1})}{16} d u_{1}$

चरण 21

एकल समाकलन को कई समाकलन में विभाजित करें.

$\frac{1}{16} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) - \frac{1}{32} (\int d u_{1} + \int \cos (2 u_{1}) d u_{1}) + \int \frac{1}{16} d u_{1} + \int - \frac{\cos (u_{1})}{16} d u_{1}$

चरण 22

स्थिरांक नियम लागू करें.

$\frac{1}{16} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) - \frac{1}{32} (u_{1} + C + \int \cos (2 u_{1}) d u_{1}) + \int \frac{1}{16} d u_{1} + \int - \frac{\cos (u_{1})}{16} d u_{1}$

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.

$\frac{1}{16} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) - \frac{1}{32} (u_{1} + C + \int \cos (u_{3}) \frac{1}{2} d u_{3}) + \int \frac{1}{16} d u_{1} + \int - \frac{\cos (u_{1})}{16} d u_{1}$

चरण 24

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

$\frac{1}{16} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) - \frac{1}{32} (u_{1} + C + \int \frac{\cos (u_{3})}{2} d u_{3}) + \int \frac{1}{16} d u_{1} + \int - \frac{\cos (u_{1})}{16} d u_{1}$

चरण 25

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

$\frac{1}{16} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) - \frac{1}{32} (u_{1} + C + \frac{1}{2} \int \cos (u_{3}) d u_{3}) + \int \frac{1}{16} d u_{1} + \int - \frac{\cos (u_{1})}{16} d u_{1}$

चरण 26

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

$\frac{1}{16} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) - \frac{1}{32} (u_{1} + C + \frac{1}{2} (\sin (u_{3}) + C)) + \int \frac{1}{16} d u_{1} + \int - \frac{\cos (u_{1})}{16} d u_{1}$

चरण 27

स्थिरांक नियम लागू करें.

$\frac{1}{16} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) - \frac{1}{32} (u_{1} + C + \frac{1}{2} (\sin (u_{3}) + C)) + \frac{1}{16} u_{1} + C + \int - \frac{\cos (u_{1})}{16} d u_{1}$

चरण 28

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

$\frac{1}{16} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) - \frac{1}{32} (u_{1} + C + \frac{1}{2} (\sin (u_{3}) + C)) + \frac{1}{16} u_{1} + C - \int \frac{\cos (u_{1})}{16} d u_{1}$

चरण 29

चूँकि $\frac{1}{16}$ बटे $u_{1}$ अचर है, $\frac{1}{16}$ को समाकलन से हटा दें.

$\frac{1}{16} (u_{2} + C - (\frac{{u_{2}}^{3}}{3} + C)) - \frac{1}{32} (u_{1} + C + \frac{1}{2} (\sin (u_{3}) + C)) + \frac{1}{16} u_{1} + C - (\frac{1}{16} \int \cos (u_{1}) d u_{1})$

चरण 30

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

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

चरण 31

सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 31.1

सरल करें.

$\frac{u_{2}}{16} - \frac{{u_{2}}^{3}}{48} - \frac{u_{1}}{32} - \frac{\sin (u_{3})}{64} + \frac{u_{1}}{16} - \frac{1}{16} \sin (u_{1}) + C$

चरण 31.2

सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 31.2.1

$\frac{u_{1}}{16}$ को एक सामान्य भाजक वाली भिन्न के रूप में लिखने के लिए, $\frac{2}{2}$ से गुणा करें.

$\frac{u_{2}}{16} - \frac{{u_{2}}^{3}}{48} - \frac{u_{1}}{32} + \frac{u_{1}}{16} \cdot \frac{2}{2} - \frac{\sin (u_{3})}{64} - \frac{1}{16} \sin (u_{1}) + C$

चरण 31.2.2

प्रत्येक व्यंजक को $32$ के सामान्य भाजक के साथ लिखें, प्रत्येक को $1$ के उपयुक्त गुणनखंड से गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 31.2.2.1

$\frac{u_{1}}{16}$ को $\frac{2}{2}$ से गुणा करें.

$\frac{u_{2}}{16} - \frac{{u_{2}}^{3}}{48} - \frac{u_{1}}{32} + \frac{u_{1} \cdot 2}{16 \cdot 2} - \frac{\sin (u_{3})}{64} - \frac{1}{16} \sin (u_{1}) + C$

चरण 31.2.2.2

$16$ को $2$ से गुणा करें.

$\frac{u_{2}}{16} - \frac{{u_{2}}^{3}}{48} - \frac{u_{1}}{32} + \frac{u_{1} \cdot 2}{32} - \frac{\sin (u_{3})}{64} - \frac{1}{16} \sin (u_{1}) + C$

चरण 31.2.3

सामान्य भाजक पर न्यूमेरेटरों को जोड़ें.

$\frac{u_{2}}{16} - \frac{{u_{2}}^{3}}{48} + \frac{- u_{1} + u_{1} \cdot 2}{32} - \frac{\sin (u_{3})}{64} - \frac{1}{16} \sin (u_{1}) + C$

चरण 31.2.4

$2$ को $u_{1}$ के बाईं ओर ले जाएं.

$\frac{u_{2}}{16} - \frac{{u_{2}}^{3}}{48} + \frac{- u_{1} + 2 \cdot u_{1}}{32} - \frac{\sin (u_{3})}{64} - \frac{1}{16} \sin (u_{1}) + C$

चरण 31.2.5

$- u_{1}$ और $2 u_{1}$ जोड़ें.

$\frac{u_{2}}{16} - \frac{{u_{2}}^{3}}{48} + \frac{u_{1}}{32} - \frac{\sin (u_{3})}{64} - \frac{1}{16} \sin (u_{1}) + C$

चरण 32

प्रत्येक एकीकरण प्रतिस्थापन चर के लिए वापस प्रतिस्थापित करें.

और स्टेप्स के लिए टैप करें…

चरण 32.1

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

$\frac{\sin (u_{1})}{16} - \frac{\sin^{3} (u_{1})}{48} + \frac{u_{1}}{32} - \frac{\sin (u_{3})}{64} - \frac{1}{16} \sin (u_{1}) + C$

चरण 32.2

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

$\frac{\sin (2 x)}{16} - \frac{\sin^{3} (2 x)}{48} + \frac{2 x}{32} - \frac{\sin (u_{3})}{64} - \frac{1}{16} \sin (2 x) + C$

चरण 32.3

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

$\frac{\sin (2 x)}{16} - \frac{\sin^{3} (2 x)}{48} + \frac{2 x}{32} - \frac{\sin (2 u_{1})}{64} - \frac{1}{16} \sin (2 x) + C$

चरण 32.4

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

$\frac{\sin (2 x)}{16} - \frac{\sin^{3} (2 x)}{48} + \frac{2 x}{32} - \frac{\sin (2 (2 x))}{64} - \frac{1}{16} \sin (2 x) + C$

चरण 33

सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 33.1

उभयनिष्ठ गुणनखंडों को रद्द करके व्यंजक $\frac{2 x}{32}$ को छोटा करें.

और स्टेप्स के लिए टैप करें…

चरण 33.1.1

$2 x$ में से $2$ का गुणनखंड करें.

$\frac{\sin (2 x)}{16} - \frac{\sin^{3} (2 x)}{48} + \frac{2 (x)}{32} - \frac{\sin (2 (2 x))}{64} - \frac{1}{16} \sin (2 x) + C$

चरण 33.1.2

$32$ में से $2$ का गुणनखंड करें.

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

चरण 33.1.3

उभयनिष्ठ गुणनखंड रद्द करें.

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

चरण 33.1.4

व्यंजक को फिर से लिखें.

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

चरण 33.2

$2$ को $2$ से गुणा करें.

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

चरण 33.3

$\sin (2 x)$ और $\frac{1}{16}$ को मिलाएं.

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

चरण 34

पदों को पुन: व्यवस्थित करें

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