JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

I=\int \frac{e^{\tan ^{-1}} x}{\left(1+x^2\right)}\left\{\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right\} d x.

Then,

View answer and explanation

Correct option: B

I=e^{\tan ^{-1} x}\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+C

Option B is correct because the integral simplifies to

e^{\tan ^{-1} x}\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+C

after a suitable substitution and simplification using trigonometric identities.

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