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If I=∫ sin 3 ...

Question

If $I = \int ({sin}^{3} x + {cos}^{2} x \cdot sin x) d x,$ then the value of $I$ is
(where $C$ is constant of integration)

A

sin x + C

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B

cot x + C

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C

tan x + C

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D

- cos x + C

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Solution

The correct option is D $- cos x + C$
$I = \int sin x ({sin}^{2} x + {cos}^{2} x) d x$
$\Rightarrow I = \int (sin x \cdot 1) d x = - cos x + C$

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