Write a value


Write a value of $\int e^{\log \sin x} \cos x d x$.


given $\int e^{\log \sin x} \cos x d x$

$=\int \sin x \cos x d x\left(\because e^{\log x}=x\right)$

Let $\sin x=t$

Differentiating on both sides we get,

$\cos x d x=d t$

Substituting above equations in given equation we get,

$=\int \mathrm{t} \mathrm{dt}$


$=\frac{\sin ^{2} x}{2}+c$

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