JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{e^x}{\left(1+e^{2 x}\right)^2} d x=

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Correct option: C

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

Option C (

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

) is correct because by substituting

t=e^x

and then

t=\tan \theta

, we can evaluate the integral.

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