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Get Answers to all your Questions
Q: Integrate the function $\cos ^3 x e^{\log \sin x}$.
Answers (1)
Given, $\cos ^3 x e^{\log \sin x}$
Let $I=\int \cos ^3 x e^{\log \sin x}$
Let $\cos x=t \Longrightarrow-\sin x d x=d t \Longrightarrow \sin x d x=-d t$ using the above substitution the integral is written as
$\therefore \int \cos ^3 x e^{\log \sin x} d x=\int \cos ^3 x \cdot \sin x d x$
$=\int \mathrm{t}^3 \cdot(-\mathrm{dt})$
$=-\int \mathrm{t}^3\cdot \mathrm{dt}$
$=-\frac{\mathrm{t}^4}{4}+\mathrm{C}$
$=-\frac{\cos ^4 \mathrm{x}}{4}+\mathrm{C}$
$I=-\frac{\cos ^4 x}{4}+C$
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