Let I(x) = ∫ (x+1)/x(1+x e^x)² dx, x > 0. If lim_(x → ∞) I(x) = 0… | JEE Main 2023 Mathematics PYQ | Jeeify

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MCQMediumJEE Main 2023 · 8 April, Shift 1Integration Techniques (Substitution, Parts, Partial Fractions)

Let $I(x) = \int \frac{x+1}{x(1+x e^x)^2} \, dx$ , $x > 0$ . If $\lim_{x \to \infty} I(x) = 0$ , then $I(1)$ is equal to:

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

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