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JEE Main 2026 · MathsMultiple choiceSingle correctHardCalculation

JEE Main 5 April 2026, Shift 1, Maths Q18

Question 18 of 75 in this shift, Maths question 18 of 25, Section A.

The value of the integral

\int_0^{\infty} \frac{\log_e(x)}{x^2+4}\,dx

is:

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

Official answer

Option 2

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Reciprocal Substitution (x = 1/t)

Same idea in other shifts

Asked 2× in all

26 Feb 2021, Shift 2 · Q80For $x>0$ , if $f(x)=\int_1^x \frac{\log_e t}{(1+t)}dt$ , then $f(e)+f\left(\frac{1}{e}\right)$ is equal to :MediumSingle 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.