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Integrate the function
$\int \cos ^3 x \mathrm{e}^{\log \sin x} d x=1(s a y)$
$\int \cos ^3 x \mathrm{e}^{\log \sin x} d x=1(s a y)$
Solution:
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Verified Answer
$\mathrm{I}=\int \cos ^3 \mathrm{x} \cdot \sin \mathrm{xdx}$
Put $\cos \mathrm{x}=\mathrm{t}, \Rightarrow-\sin \mathrm{xdx}=\mathrm{dt}$
$\therefore \mathrm{I}=-\int \mathrm{t}^3 \mathrm{dt}=-\frac{\mathrm{t}^4}{4}+\mathrm{c}=-\frac{1}{4} \cos ^4 \mathrm{x}+\mathrm{c}$
Put $\cos \mathrm{x}=\mathrm{t}, \Rightarrow-\sin \mathrm{xdx}=\mathrm{dt}$
$\therefore \mathrm{I}=-\int \mathrm{t}^3 \mathrm{dt}=-\frac{\mathrm{t}^4}{4}+\mathrm{c}=-\frac{1}{4} \cos ^4 \mathrm{x}+\mathrm{c}$
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