Integration Problem with Limit Condition

JEE MAIN 2023

8/4/2023 s1

Question

Let $I(x)=\int \frac{(x+1)}{x\left(1+x e^x\right)^2} d x, x>0$, If $\lim _{x \rightarrow \infty} I(x)=0$, then $I(1)$ is equal to

Select the correct option:

$\frac{e+1}{e+2}-\log _e(e+1)$

$\frac{e+1}{e+2}+\log _e(e+1)$

$\frac{e+2}{e+1}+\log _e(e+1)$

$\frac{\mathrm{e}+2}{\mathrm{e}+1}-\log _{\mathrm{e}}(\mathrm{e}+1)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Medium

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