JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

The value of

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

, is equal to

View answer and explanation

Correct option: B

\log \left|\frac{x e^x}{1+x e^x}\right|+\frac{1}{1+x e^x}+C

Option B is correct because after substituting

1+xe^x = t

and using partial fractions, the integral evaluates to

\log \left|\frac{x e^x}{1+x e^x}\right|+\frac{1}{1+x e^x}+C

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