JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\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

(x>0)

is equal to

View answer and explanation

Correct option: C

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

Option C (

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

) is correct because after simplification and substitution, the integral can be solved to obtain this result.

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