JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 6 April 2026, Shift 2, Maths Q20

Question 20 of 75 in this shift, Maths question 20 of 25, Section A.

The value of the integral

\int_{-1}^{1}\left(\frac{x^3+|x|+1}{x^2+2|x|+1}\right)dx

is equal to :

(1) $3\log_e 2$
(2) $2\log_e 2$ Official answer
(3) $5\log_e 3$
(4) $3\log_e 3$

Official answer

Option 2

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Even and Odd Functions

Same idea in other shifts

Asked 3× in all

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18 Mar 2021, Shift 1 · Q82Let $f(x)$ and $g(x)$ be two functions satisfying $f(x^2)+g(4-x)=4x^3$ and $g(4-x)+g(x)=0$ , then the value of $\int_{-4}^{4}f(x^2)\,dx$ is…HardNumerical value

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.