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Question Number 97322 by student work last updated on 07/Jun/20

$$\int \sin {}^4\mathrm{x}\cdot \cos {}^5\mathrm{xdx}=?$$

Answered by bemath last updated on 08/Jun/20

$$\int \sin {}^{4}x{(1-\sin {}^{2}x)}^2\cos xdx$$$$=\int q^4{(1-q^2)}^{2}dq$$$$=\int q^4(1-2q^2+q^4)dq$$$$=\int q^4-2q^6+q^{8}dq$$$$=\frac{1}{5}\sin {}^{5}x-\frac{2}{7}\sin {}^{7}x+\frac{1}{9}\sin {}^{9}x+c$$

Commented by Aziztisffola last updated on 07/Jun/20

$$\frac{2}{7}{\sin }^7\left(\mathrm{x}\right)$$

Commented by Rohit@Thakur last updated on 07/Jun/20

$$\frac{2}{7}{sin}^7\left(x\right)$$

Commented by bemath last updated on 08/Jun/20

$$\mathrm{yes}.\mathrm{typo}$$

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