JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

The value of

\int \frac{\left(\tan ^{-1}(\sin x+1)\right) \cos x}{\left(3+2 \sin x-\cos ^2 x\right)} d x

is (where

\mathrm{c}

is the constant integration)

View answer and explanation

Correct option: C

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

Option C (

\frac{{(\tan^{-1}(\sin x+1))^2}}{{2}}+c

) is correct because it is the result of the integration after a suitable substitution.

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