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Question Number 78265 by msup trace by abdo last updated on 15/Jan/20

$$find\int \frac{{sin}^{3}x}{{tan}^{5}x}dx$$

Answered by jagoll last updated on 15/Jan/20

$$\int \sin {}^{3}x\cot {}^{5}xdx=$$$$\int \frac{{(1-\sin {}^{2}x)}^2\cos xdx}{\sin {}^{2}x}=$$$$\int \frac{{(1-{\sin }^{2}x)}^2}{\sin {}^{2}x}d\left(\sin x\right)$$$$$$

Commented by john santu last updated on 15/Jan/20

$$=\int \frac{1-2\sin {}^{2}x+\sin {}^{4}x}{\sin {}^{2}x}d\left(\sin x\right)$$$$=-\frac{1}{\sin x}-2\sin x+\frac{1}{3}\sin {}^{3}x+c$$

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