JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

I=\int \frac{1}{\sqrt{1-e^{2 x}}} d x

is equal to

View answer and explanation

Correct option: C

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

Option C is correct because the integral simplifies to

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

after substitution and simplification using trigonometric identities.

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