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

Langkah 1

Sederhanakan dengan memfaktorkan.

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Langkah 1.1

Faktorkan $2$ dari $4$ .

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

Langkah 1.2

Tulis kembali ${\cos (x)}^{2 (2)}$ sebagai eksponensiasi.

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

Langkah 2

Gunakan rumus setengah sudut untuk menuliskan kembali $\cos^{2} (x)$ sebagai $\frac{1 + \cos (2 x)}{2}$ .

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

Langkah 3

Gunakan rumus setengah sudut untuk menuliskan kembali $\sin^{2} (x)$ sebagai $\frac{1 - \cos (2 x)}{2}$ .

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

Langkah 4

Biarkan $u_{1} = 2 x$ . Kemudian $d u_{1} = 2 d x$ sehingga $\frac{1}{2} d u_{1} = d x$ . Tulis kembali menggunakan $u_{1}$ dan $d$ $u_{1}$ .

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Langkah 4.1

Biarkan $u_{1} = 2 x$ . Tentukan $\frac{d u_{1}}{d x}$ .

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Langkah 4.1.1

Diferensialkan $2 x$ .

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

Langkah 4.1.2

Karena $2$ konstan terhadap $x$ , turunan dari $2 x$ terhadap $x$ adalah $2 \frac{d}{d x} [x]$ .

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

Langkah 4.1.3

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d x} [x^{n}]$ adalah $n x^{n - 1}$ di mana $n = 1$ .

$2 \cdot 1$

Langkah 4.1.4

Kalikan $2$ dengan $1$ .

$2$

Langkah 4.2

Tulis kembali soalnya menggunakan $u_{1}$ dan $d u_{1}$ .

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

Langkah 5

Sederhanakan dengan mengalikan semuanya.

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Langkah 5.1

Sederhanakan.

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Langkah 5.1.1

Kalikan $\frac{1}{2}$ dengan $\frac{1 - \cos (u_{1})}{2}$ .

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

Langkah 5.1.2

Kalikan $2$ dengan $2$ .

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

Langkah 5.2

Sederhanakan dengan saling menukar.

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Langkah 5.2.1

Tulis kembali $\frac{1 - \cos (u_{1})}{4}$ sebagai hasil kali.

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

Langkah 5.2.2

Tulis kembali $\frac{1 + \cos (u_{1})}{2}$ sebagai hasil kali.

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

Langkah 5.3

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

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Langkah 5.3.1

Tulis kembali eksponensiasinya sebagai hasil kali.

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

Langkah 5.3.2

Terapkan sifat distributif.

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

Langkah 5.3.3

Terapkan sifat distributif.

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

Langkah 5.3.4

Terapkan sifat distributif.

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

Langkah 5.3.5

Terapkan sifat distributif.

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

Langkah 5.3.6

Terapkan sifat distributif.

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

Langkah 5.3.7

Terapkan sifat distributif.

Langkah 5.3.8

Terapkan sifat distributif.

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

Langkah 5.3.9

Terapkan sifat distributif.

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

Langkah 5.3.10

Terapkan sifat distributif.

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

Langkah 5.3.11

Terapkan sifat distributif.

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

Langkah 5.3.12

Terapkan sifat distributif.

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

Langkah 5.3.13

Terapkan sifat distributif.

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

Langkah 5.3.14

Terapkan sifat distributif.

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

Langkah 5.3.15

Susun kembali $\frac{1}{4}$ dan $1$ .

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

Langkah 5.3.16

Susun kembali $\frac{1}{2}$ dan $1$ .

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

Langkah 5.3.17

Susun kembali $\frac{1}{2}$ dan $1$ .

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

Langkah 5.3.18

Pindahkan $\frac{1}{2}$ .

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

Langkah 5.3.19

Pindahkan tanda kurung.

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

Langkah 5.3.20

Pindahkan tanda kurung.

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

Langkah 5.3.21

Pindahkan $\frac{1}{4}$ .

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

Langkah 5.3.22

Susun kembali $\frac{1}{4}$ dan $1$ .

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

Langkah 5.3.23

Susun kembali $\frac{1}{2}$ dan $1$ .

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

Langkah 5.3.24

Pindahkan tanda kurung.

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

Langkah 5.3.25

Pindahkan tanda kurung.

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

Langkah 5.3.26

Pindahkan $\frac{1}{4}$ .

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

Langkah 5.3.27

Susun kembali $\frac{1}{4}$ dan $1$ .

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

Langkah 5.3.28

Susun kembali $\frac{1}{2}$ dan $1$ .

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

Langkah 5.3.29

Pindahkan $\cos (u_{1})$ .

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

Langkah 5.3.30

Susun kembali $\frac{1}{2}$ dan $1$ .

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

Langkah 5.3.31

Pindahkan tanda kurung.

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

Langkah 5.3.32

Pindahkan tanda kurung.

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

Langkah 5.3.33

Pindahkan $\frac{1}{4}$ .

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

Langkah 5.3.34

Susun kembali $\frac{1}{4}$ dan $1$ .

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

Langkah 5.3.35

Pindahkan tanda kurung.

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

Langkah 5.3.36

Pindahkan tanda kurung.

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

Langkah 5.3.37

Susun kembali $\frac{1}{4}$ dan $- 1$ .

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

Langkah 5.3.38

Susun kembali $\frac{1}{2}$ dan $1$ .

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

Langkah 5.3.39

Susun kembali $\frac{1}{2}$ dan $1$ .

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

Langkah 5.3.40

Pindahkan $\frac{1}{2}$ .

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

Langkah 5.3.41

Pindahkan tanda kurung.

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

Langkah 5.3.42

Pindahkan tanda kurung.

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

Langkah 5.3.43

Pindahkan $\cos (u_{1})$ .

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

Langkah 5.3.44

Pindahkan $\frac{1}{4}$ .

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

Langkah 5.3.45

Susun kembali $\frac{1}{4}$ dan $- 1$ .

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

Langkah 5.3.46

Susun kembali $\frac{1}{2}$ dan $1$ .

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

Langkah 5.3.47

Pindahkan tanda kurung.

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

Langkah 5.3.48

Pindahkan tanda kurung.

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

Langkah 5.3.49

Pindahkan $\cos (u_{1})$ .

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

Langkah 5.3.50

Pindahkan $\frac{1}{4}$ .

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

Langkah 5.3.51

Susun kembali $\frac{1}{4}$ dan $- 1$ .

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

Langkah 5.3.52

Susun kembali $\frac{1}{2}$ dan $1$ .

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

Langkah 5.3.53

Pindahkan $\cos (u_{1})$ .

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

Langkah 5.3.54

Susun kembali $\frac{1}{2}$ dan $1$ .

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

Langkah 5.3.55

Pindahkan tanda kurung.

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

Langkah 5.3.56

Pindahkan tanda kurung.

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

Langkah 5.3.57

Pindahkan $\cos (u_{1})$ .

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

Langkah 5.3.58

Pindahkan $\frac{1}{4}$ .

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

Langkah 5.3.59

Susun kembali $\frac{1}{4}$ dan $- 1$ .

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

Langkah 5.3.60

Pindahkan tanda kurung.

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

Langkah 5.3.61

Pindahkan tanda kurung.

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

Langkah 5.3.62

Kalikan $1$ dengan $1$ .

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

Langkah 5.3.63

Kalikan $1$ dengan $1$ .

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

Langkah 5.3.64

Kalikan $\frac{1}{4}$ dengan $1$ .

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

Langkah 5.3.65

Kalikan $\frac{1}{4}$ dengan $\frac{1}{2}$ .

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

Langkah 5.3.66

Kalikan $4$ dengan $2$ .

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

Langkah 5.3.67

Kalikan $\frac{1}{8}$ dengan $\frac{1}{2}$ .

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

Langkah 5.3.68

Kalikan $8$ dengan $2$ .

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

Langkah 5.3.69

Kalikan $1$ dengan $1$ .

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

Langkah 5.3.70

Kalikan $\frac{1}{4}$ dengan $1$ .

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

Langkah 5.3.71

Kalikan $\frac{1}{4}$ dengan $\frac{1}{2}$ .

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

Langkah 5.3.72

Kalikan $4$ dengan $2$ .

$\int \frac{1}{16} + \frac{1}{8} \cdot \frac{1}{2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.73

Kalikan $\frac{1}{8}$ dengan $\frac{1}{2}$ .

$\int \frac{1}{16} + \frac{1}{8 \cdot 2} \cos (u_{1}) + 1 \cdot 1 \frac{1}{4} \frac{1}{2} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.74

Kalikan $8$ dengan $2$ .

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

Langkah 5.3.75

Gabungkan $\frac{1}{16}$ dan $\cos (u_{1})$ .

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

Langkah 5.3.76

Kalikan $1$ dengan $1$ .

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

Langkah 5.3.77

Kalikan $\frac{1}{4}$ dengan $1$ .

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

Langkah 5.3.78

Kalikan $\frac{1}{4}$ dengan $\frac{1}{2}$ .

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

Langkah 5.3.79

Kalikan $4$ dengan $2$ .

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{1}{8} \cos (u_{1}) \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.80

Gabungkan $\frac{1}{8}$ dan $\cos (u_{1})$ .

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{8} \cdot \frac{1}{2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.81

Kalikan $\frac{\cos (u_{1})}{8}$ dengan $\frac{1}{2}$ .

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{8 \cdot 2} + 1 (\frac{1}{4}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.82

Kalikan $8$ dengan $2$ .

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

Langkah 5.3.83

Kalikan $\frac{1}{4}$ dengan $1$ .

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

Langkah 5.3.84

Kalikan $\frac{1}{4}$ dengan $\frac{1}{2}$ .

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

Langkah 5.3.85

Kalikan $4$ dengan $2$ .

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{1}{8} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.86

Gabungkan $\frac{1}{8}$ dan $\cos (u_{1})$ .

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{8} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.87

Kalikan $\frac{\cos (u_{1})}{8}$ dengan $\frac{1}{2}$ .

$\int \frac{1}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{16} + \frac{\cos (u_{1})}{8 \cdot 2} \cos (u_{1}) - 1 \cdot 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.88

Kalikan $8$ dengan $2$ .

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

Langkah 5.3.89

Gabungkan $\frac{\cos (u_{1})}{16}$ dan $\cos (u_{1})$ .

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

Langkah 5.3.90

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

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

Langkah 5.3.91

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

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

Langkah 5.3.92

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

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

Langkah 5.3.93

Tambahkan $1$ dan $1$ .

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

Langkah 5.3.94

Tambahkan $\frac{\cos (u_{1})}{16}$ dan $\frac{\cos (u_{1})}{16}$ .

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

Langkah 5.3.95

Gabungkan $2$ dan $\frac{\cos (u_{1})}{16}$ .

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

Langkah 5.3.96

Kalikan $- 1$ dengan $1$ .

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

Langkah 5.3.97

Kalikan $- 1$ dengan $1$ .

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

Langkah 5.3.98

Gabungkan $\frac{1}{4}$ dan $\cos (u_{1})$ .

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

Langkah 5.3.99

Gabungkan $- \frac{\cos (u_{1})}{4}$ dan $\frac{1}{2}$ .

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

Langkah 5.3.100

Kalikan $4$ dengan $2$ .

$\int \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{8} \cdot \frac{1}{2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.101

Gabungkan $- \frac{\cos (u_{1})}{8}$ dan $\frac{1}{2}$ .

$\int \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{8 \cdot 2} - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.102

Kalikan $8$ dengan $2$ .

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

Langkah 5.3.103

Kalikan $- 1$ dengan $1$ .

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

Langkah 5.3.104

Gabungkan $\frac{1}{4}$ dan $\cos (u_{1})$ .

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

Langkah 5.3.105

Gabungkan $- \frac{\cos (u_{1})}{4}$ dan $\frac{1}{2}$ .

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

Langkah 5.3.106

Kalikan $4$ dengan $2$ .

$\int \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{8} \cdot \frac{1}{2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.107

Gabungkan $- \frac{\cos (u_{1})}{8}$ dan $\frac{1}{2}$ .

$\int \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos (u_{1})}{8 \cdot 2} \cos (u_{1}) - 1 \cdot 1 \frac{1}{4} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.108

Kalikan $8$ dengan $2$ .

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

Langkah 5.3.109

Gabungkan $\frac{\cos (u_{1})}{16}$ dan $\cos (u_{1})$ .

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

Langkah 5.3.110

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

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

Langkah 5.3.111

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

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

Langkah 5.3.112

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

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

Langkah 5.3.113

Tambahkan $1$ dan $1$ .

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

Langkah 5.3.114

Kalikan $- 1$ dengan $1$ .

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

Langkah 5.3.115

Gabungkan $\frac{1}{4}$ dan $\cos (u_{1})$ .

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

Langkah 5.3.116

Gabungkan $- \frac{\cos (u_{1})}{4}$ dan $\frac{1}{2}$ .

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

Langkah 5.3.117

Kalikan $4$ dengan $2$ .

$\int \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{8} \cos (u_{1}) \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.118

Gabungkan $\frac{\cos (u_{1})}{8}$ dan $\cos (u_{1})$ .

$\int \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1}) \cos (u_{1})}{8} \cdot \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.119

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

$\int \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{1} (u_{1}) \cos (u_{1})}{8} \cdot \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.120

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

$\int \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{1} (u_{1}) \cos^{1} (u_{1})}{8} \cdot \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.121

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$\int \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{{\cos (u_{1})}^{1 + 1}}{8} \cdot \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.122

Tambahkan $1$ dan $1$ .

$\int \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{8} \cdot \frac{1}{2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.123

Gabungkan $- \frac{\cos^{2} (u_{1})}{8}$ dan $\frac{1}{2}$ .

$\int \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{16} - \frac{\cos^{2} (u_{1})}{8 \cdot 2} - 1 (\frac{1}{4}) \cos (u_{1}) \frac{1}{2} \cos (u_{1}) \frac{1}{2} \cos (u_{1}) d u_{1}$

Langkah 5.3.124

Kalikan $8$ dengan $2$ .

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

Langkah 5.3.125

Gabungkan $\frac{1}{4}$ dan $\cos (u_{1})$ .

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

Langkah 5.3.126

Gabungkan $- 1 \frac{\cos (u_{1})}{4}$ dan $\frac{1}{2}$ .

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

Langkah 5.3.127

Gabungkan $\frac{- 1 \frac{\cos (u_{1})}{4}}{2}$ dan $\cos (u_{1})$ .

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

Langkah 5.3.128

Gabungkan $\frac{\cos (u_{1})}{4}$ dan $\cos (u_{1})$ .

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

Langkah 5.3.129

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

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

Langkah 5.3.130

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

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

Langkah 5.3.131

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

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

Langkah 5.3.132

Tambahkan $1$ dan $1$ .

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

Langkah 5.3.133

Kalikan $\frac{- 1 \frac{\cos^{2} (u_{1})}{4}}{2}$ dengan $\frac{1}{2}$ .

Langkah 5.3.134

Kalikan $2$ dengan $2$ .

Langkah 5.3.135

Gabungkan $\frac{- 1 \frac{\cos^{2} (u_{1})}{4}}{4}$ dan $\cos (u_{1})$ .

Langkah 5.3.136

Gabungkan $\frac{\cos^{2} (u_{1})}{4}$ dan $\cos (u_{1})$ .

Langkah 5.3.137

Naikkan $\cos (u_{1})$ menjadi pangkat $1$ .

Langkah 5.3.138

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

Langkah 5.3.139

Tambahkan $2$ dan $1$ .

Langkah 5.3.140

Kurangi $\frac{\cos^{2} (u_{1})}{16}$ dengan $- \frac{\cos^{2} (u_{1})}{16}$ .

$\int \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} - 2 \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} d u_{1}$

Langkah 5.3.141

Gabungkan $- 2$ dan $\frac{\cos^{2} (u_{1})}{16}$ .

$\int \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{\cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} + \frac{- 2 \cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} d u_{1}$

Langkah 5.3.142

Susun kembali $\frac{2 \cos (u_{1})}{16}$ dan $\frac{\cos^{2} (u_{1})}{16}$ .

$\int \frac{1}{16} + \frac{\cos^{2} (u_{1})}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} + \frac{- 2 \cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} d u_{1}$

Langkah 5.3.143

Susun kembali $\frac{1}{16}$ dan $\frac{\cos^{2} (u_{1})}{16}$ .

$\int \frac{\cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} + \frac{- 2 \cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} d u_{1}$

Langkah 5.3.144

Susun kembali $\frac{- 2 \cos^{2} (u_{1})}{16}$ dan $\frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4}$ .

$\int \frac{\cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- 2 \cos^{2} (u_{1})}{16} d u_{1}$

Langkah 5.3.145

Pindahkan $- \frac{\cos (u_{1})}{16}$ .

$\int \frac{\cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- 2 \cos^{2} (u_{1})}{16} - \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 5.3.146

Pindahkan $\frac{2 \cos (u_{1})}{16}$ .

$\int \frac{\cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- 2 \cos^{2} (u_{1})}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 5.3.147

Pindahkan $\frac{1}{16}$ .

$\int \frac{\cos^{2} (u_{1})}{16} + \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- 2 \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 5.3.148

Susun kembali $\frac{\cos^{2} (u_{1})}{16}$ dan $\frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4}$ .

$\int \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{\cos^{2} (u_{1})}{16} + \frac{- 2 \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 5.3.149

Gabungkan pembilang dari penyebut persekutuan.

$\int \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{\cos^{2} (u_{1}) - 2 \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 5.3.150

Kurangi $2 \cos^{2} (u_{1})$ dengan $\cos^{2} (u_{1})$ .

$\int \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1})}{16} - \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 5.3.151

Gabungkan pembilang dari penyebut persekutuan.

$\int \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{2 \cos (u_{1}) - \cos (u_{1})}{16} d u_{1}$

Langkah 5.3.152

Kurangi $\cos (u_{1})$ dengan $2 \cos (u_{1})$ .

$\int \frac{- 1 \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 5.4

Sederhanakan.

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Langkah 5.4.1

Tulis kembali $- 1 \frac{\cos^{3} (u_{1})}{4}$ sebagai $- \frac{\cos^{3} (u_{1})}{4}$ .

$\int \frac{- \frac{\cos^{3} (u_{1})}{4}}{4} + \frac{- \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 5.4.2

Tulis kembali $\frac{- \frac{\cos^{3} (u_{1})}{4}}{4}$ sebagai hasil kali.

$\int - \frac{\cos^{3} (u_{1})}{4} \cdot \frac{1}{4} + \frac{- \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 5.4.3

Kalikan $\frac{1}{4}$ dengan $\frac{\cos^{3} (u_{1})}{4}$ .

$\int - \frac{\cos^{3} (u_{1})}{4 \cdot 4} + \frac{- \cos^{2} (u_{1})}{16} + \frac{1}{16} + \frac{\cos (u_{1})}{16} d u_{1}$

Langkah 5.4.4

Kalikan $4$ dengan $4$ .

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

Langkah 5.4.5

Pindahkan tanda negatif di depan pecahan.

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

Langkah 6

Bagi integral tunggal menjadi beberapa integral.

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

Langkah 7

Karena $- 1$ konstan terhadap $u_{1}$ , pindahkan $- 1$ keluar dari integral.

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

Langkah 8

Karena $\frac{1}{16}$ konstan terhadap $u_{1}$ , pindahkan $\frac{1}{16}$ keluar dari integral.

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

Langkah 9

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

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

Langkah 10

Menggunakan Identitas Pythagoras, tulis kembali $\cos^{2} (u_{1})$ sebagai $1 - \sin^{2} (u_{1})$ .

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

Langkah 11

Biarkan $u_{2} = \sin (u_{1})$ . Kemudian $d u_{2} = \cos (u_{1}) d u_{1}$ sehingga $\frac{1}{\cos (u_{1})} d u_{2} = d u_{1}$ . Tulis kembali menggunakan $u_{2}$ dan $d$ $u_{2}$ .

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Langkah 11.1

Biarkan $u_{2} = \sin (u_{1})$ . Tentukan $\frac{d u_{2}}{d u_{1}}$ .

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Langkah 11.1.1

Diferensialkan $\sin (u_{1})$ .

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

Langkah 11.1.2

Turunan dari $\sin (u_{1})$ terhadap $u_{1}$ adalah $\cos (u_{1})$ .

$\cos (u_{1})$

Langkah 11.2

Tulis kembali soalnya menggunakan $u_{2}$ dan $d u_{2}$ .

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

Langkah 12

Bagi integral tunggal menjadi beberapa integral.

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

Langkah 13

Terapkan aturan konstanta.

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

Langkah 14

Karena $- 1$ konstan terhadap $u_{2}$ , pindahkan $- 1$ keluar dari integral.

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

Langkah 15

Menurut Kaidah Pangkat, integral dari ${u_{2}}^{2}$ terhadap $u_{2}$ adalah $\frac{1}{3} {u_{2}}^{3}$ .

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

Langkah 16

Gabungkan $\frac{1}{3}$ dan ${u_{2}}^{3}$ .

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

Langkah 17

Karena $- 1$ konstan terhadap $u_{1}$ , pindahkan $- 1$ keluar dari integral.

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

Langkah 18

Karena $\frac{1}{16}$ konstan terhadap $u_{1}$ , pindahkan $\frac{1}{16}$ keluar dari integral.

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

Langkah 19

Gunakan rumus setengah sudut untuk menuliskan kembali $\cos^{2} (u_{1})$ sebagai $\frac{1 + \cos (2 u_{1})}{2}$ .

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

Langkah 20

Karena $\frac{1}{2}$ konstan terhadap $u_{1}$ , pindahkan $\frac{1}{2}$ keluar dari integral.

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

Langkah 21

Sederhanakan.

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Langkah 21.1

Kalikan $\frac{1}{2}$ dengan $\frac{1}{16}$ .

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

Langkah 21.2

Kalikan $2$ dengan $16$ .

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

Langkah 22

Bagi integral tunggal menjadi beberapa integral.

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

Langkah 23

Terapkan aturan konstanta.

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

Langkah 24

Biarkan $u_{3} = 2 u_{1}$ . Kemudian $d u_{3} = 2 d u_{1}$ sehingga $\frac{1}{2} d u_{3} = d u_{1}$ . Tulis kembali menggunakan $u_{3}$ dan $d$ $u_{3}$ .

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Langkah 24.1

Biarkan $u_{3} = 2 u_{1}$ . Tentukan $\frac{d u_{3}}{d u_{1}}$ .

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Langkah 24.1.1

Diferensialkan $2 u_{1}$ .

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

Langkah 24.1.2

Karena $2$ konstan terhadap $u_{1}$ , turunan dari $2 u_{1}$ terhadap $u_{1}$ adalah $2 \frac{d}{d u_{1}} [u_{1}]$ .

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

Langkah 24.1.3

Diferensialkan menggunakan Kaidah Pangkat yang menyatakan bahwa $\frac{d}{d u_{1}} [{u_{1}}^{n}]$ adalah $n {u_{1}}^{n - 1}$ di mana $n = 1$ .

$2 \cdot 1$

Langkah 24.1.4

Kalikan $2$ dengan $1$ .

$2$

Langkah 24.2

Tulis kembali soalnya menggunakan $u_{3}$ dan $d u_{3}$ .

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

Langkah 25

Gabungkan $\cos (u_{3})$ dan $\frac{1}{2}$ .

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

Langkah 26

Karena $\frac{1}{2}$ konstan terhadap $u_{3}$ , pindahkan $\frac{1}{2}$ keluar dari integral.

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

Langkah 27

Integral dari $\cos (u_{3})$ terhadap $u_{3}$ adalah $\sin (u_{3})$ .

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

Langkah 28

Terapkan aturan konstanta.

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

Langkah 29

Karena $\frac{1}{16}$ konstan terhadap $u_{1}$ , pindahkan $\frac{1}{16}$ keluar dari integral.

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

Langkah 30

Integral dari $\cos (u_{1})$ terhadap $u_{1}$ adalah $\sin (u_{1})$ .

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

Langkah 31

Sederhanakan.

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Langkah 31.1

Sederhanakan.

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

Langkah 31.2

Sederhanakan.

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Langkah 31.2.1

Untuk menuliskan $\frac{u_{1}}{16}$ sebagai pecahan dengan penyebut umum, kalikan dengan $\frac{2}{2}$ .

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

Langkah 31.2.2

Tulis setiap pernyataan menggunakan penyebut umum dari $32$ , dengan mengalikan masing-masing pembilang dan penyebut dengan faktor dari $1$ yang sesuai.

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Langkah 31.2.2.1

Kalikan $\frac{u_{1}}{16}$ dengan $\frac{2}{2}$ .

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

Langkah 31.2.2.2

Kalikan $16$ dengan $2$ .

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

Langkah 31.2.3

Gabungkan pembilang dari penyebut persekutuan.

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

Langkah 31.2.4

Pindahkan $2$ ke sebelah kiri $u_{1}$ .

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

Langkah 31.2.5

Tambahkan $- u_{1}$ dan $2 u_{1}$ .

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

Langkah 32

Substitusikan kembali untuk setiap variabel substitusi pengintegralan.

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Langkah 32.1

Ganti semua kemunculan $u_{2}$ dengan $\sin (u_{1})$ .

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

Langkah 32.2

Ganti semua kemunculan $u_{1}$ dengan $2 x$ .

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

Langkah 32.3

Ganti semua kemunculan $u_{3}$ dengan $2 u_{1}$ .

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

Langkah 32.4

Ganti semua kemunculan $u_{1}$ dengan $2 x$ .

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

Langkah 33

Sederhanakan.

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Langkah 33.1

Kurangi pernyataan $\frac{2 x}{32}$ dengan membatalkan faktor persekutuan.

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Langkah 33.1.1

Faktorkan $2$ dari $2 x$ .

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

Langkah 33.1.2

Faktorkan $2$ dari $32$ .

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

Langkah 33.1.3

Batalkan faktor persekutuan.

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

Langkah 33.1.4

Tulis kembali pernyataannya.

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

Langkah 33.2

Kalikan $2$ dengan $2$ .

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

Langkah 34

Susun kembali suku-suku.

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