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Indefinite Integrals question

2023 · 8 Apr · Shift 1 · Q32

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PYQ Library
JEE Main
Mathematics
Indefinite Integrals
2023 · 8 Apr · Shift 1 · Q32

Indefinite Integrals question

2023 · 8 Apr · Shift 1 · Q32

JEE MainMathematicsIndefinite IntegralsMCQ+4 / −1

Let

I(x)=\int \frac{(x+1)}{x\left(1+x e^{x}\right)^{2}} d x, x \gt 0

. If

\lim_{x \rightarrow \infty} I(x)=0

, then

I(1)

is equal to :

A
$\frac{e+1}{e+2}-\log _{e}(e+1)$
B
$\frac{e+1}{e+2}+\log _{e}(e+1)$
C
$\frac{e+2}{e+1}-\log _{e}(e+1)$
D
$\frac{e+2}{e+1}+\log _{e}(e+1)$

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