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 topic in other shifts

All Definite Integral Properties questions

2 Apr 2026, Shift 1 · Q19Let $[\cdot]$ denote the greatest integer function. Then the value of $\int_0^3\left(\frac{e^x+e^{-x}}{[x]!}\right)dx$ is :MediumSingle correct
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2 Apr 2026, Shift 2 · Q17The value of $\int_0^{20\pi} (\sin^4 x + \cos^4 x)dx$ is equal to:EasySingle correct
4 Apr 2026, Shift 1 · Q19Let $\int_{-2}^{2}\left(|\sin x|+[x\sin x]\right)dx=2(3-\cos 2)+\beta$ , where $[\cdot]$ is the greatest integer function. Then…HardSingle correct
6 Apr 2026, Shift 1 · Q18The value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\left(\frac{32\cos^4 x}{1+e^{\sin x}}\right)dx$ is:MediumSingle correct
6 Apr 2026, Shift 2 · Q20The value of the integral $\int_{-1}^{1}\left(\frac{x^3+|x|+1}{x^2+2|x|+1}\right)dx$ 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 42 of the 174 JEE Main shifts held from 2017 to 2026.