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JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 April 2023, Shift 1, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

Let

I(x)=\int\frac{(x+1)}{x(1+xe^x)^2}dx

,

x>0

. If

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

, then

I(1)

is equal to

(1) $\frac{e+2}{e+1}-\log_e(e+1)$ Official answer
(2) $\frac{e+2}{e+1}+\log_e(e+1)$
(3) $\frac{e+1}{e+2}-\log_e(e+1)$
(4) $\frac{e+1}{e+2}+\log_e(e+1)$

Official answer

Option 1

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Implicit Derivative Recognition

Same idea in other shifts

Asked 2× in all

4 Sep 2020, Shift 2 · Q61The integral $\int_{\pi/6}^{\pi/3} \tan^3 x \cdot \sin^2 3x \,(2\sec^2 x \cdot \sin^2 3x + 3\tan x \cdot \sin 6x)\,dx$ is equal to :HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.