Question:
Write a value of $\int e^{\log \sin x} \cos x d x$.
Solution:
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,
$=\int \mathrm{t} \mathrm{dt}$
$=\frac{t^{2}}{2}+c$
$=\frac{\sin ^{2} x}{2}+c$
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