JEE Main 2026 · 6 Apr · Shift 2 · Mathematics Q20

MathematicsSingle correct+4 / -1Question 20 of 75

The value of the integral $\displaystyle\int_{-1}^1\left(\frac{x^3+|x|+1}{x^2+2|x|+1}\right)dx$ is equal to :

3\log_e2

2\log_e2

5\log_e3

3\log_e3

Answer and worked solution

Official answer: B

Odd part. $\dfrac{x^3}{x^2+2|x|+1}$ is odd and integrates to 0.

Even part. $\dfrac{|x|+1}{(|x|+1)^2}=\dfrac1{|x|+1}$ :
$2\int_0^1\frac{dx}{x+1}=2\ln2.$

(B)

Topics:Properties of definite integrals

JEE Main 2026 · 6 Apr · Shift 2, Mathematics question 20