Integrate the function in Exercise: ^ 3 x e^ - Vidyadip

Question

Integrate the function in Exercise:$\cos^{3}\text{x}\ \text{e}^{\log\sin\text{x}}$

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Answer

$\cos^{3}\ \text{xe}^{\log\sin\text{x}}=\cos^{3}\text{x}\times\sin\text{x}$
$\text{Let}\ \cos\text{x}=\text{t}\Rightarrow-\sin\text{x}\ \text{dx}=\text{dt}$
$\Rightarrow\int\cos^{3}\text{xe}^{\log\sin\text{x}}\text{dx}=\int\cos^{3}\text{x}\sin\ \text{xdx}$
$=-\int\text{t}^3\ \text{dt}$
$=-\frac{\text{t}^{4}}{4}+\text{C}$
$=-\frac{\cos^{4}\text{x}}{4}+\text{C}$

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