JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of the integral

\int e^{\sin ^2 x}\left(\cos x+\cos ^3 x\right) \sin x d x

View answer and explanation

Correct option: A

\frac{1}{2} e^{\sin ^2 x}\left(3-\sin ^2 x\right)+c

Option A (

\frac{1}{2} e^{\sin ^2 x}\left(3-\sin ^2 x\right)+c

) is correct because after substituting

t=\sin^2 x

and integrating, we obtain the given result.

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\int {e}^{{x}^2}\left(2-\frac{1}{{x}^2}\right) {de}={e}^{{x}^2} {f}({x})+{C}

{f}\left(\frac{1}{2}\right)=2

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{C}

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