JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 6 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^2(x\sec^2x+\tan x)}{(x\tan x+1)^2}\,dx

. If

I(0)=0

, then

I\left(\frac{\pi}{4}\right)

is equal to

(1) $\log_e\frac{(\pi+4)^2}{32}-\frac{\pi^2}{4(\pi+4)}$ Official answer
(2) $\log_e\frac{(\pi+4)^2}{16}+\frac{\pi^2}{4(\pi+4)}$
(3) $\log_e\frac{(\pi+4)^2}{16}-\frac{\pi^2}{4(\pi+4)}$
(4) $\log_e\frac{(\pi+4)^2}{32}+\frac{\pi^2}{4(\pi+4)}$

Official answer

Option 1

NTA final key.

Chapter: Integrals
Topic: Integration by Parts
Idea tested: Generalized Reverse Product Rule

Same topic in other shifts

All Integration by Parts questions

2 Apr 2025, Shift 2 · Q18 $4\int_0^1 \left(\frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}}\right)\mathrm{d}x - 3\log_e(\sqrt{3})$ is equal to :HardSingle correct
9 Apr 2024, Shift 2 · Q12The value of the integral $\int_{-1}^{2}\log_e\left(x+\sqrt{x^2+1}\right)dx$ isMediumSingle correct
11 Apr 2023, Shift 1 · Q15The value of the integral $\int_{-\log_e 2}^{\log_e 2} e^x\left(\log_e\left(e^x + \sqrt{1+e^{2x}}\right)\right)dx$ is equal toHardSingle correct
11 Apr 2023, Shift 1 · Q26For $m, n > 0$ , let $\alpha(m, n) = \int_0^2 t^m(1+3t)^n\,dt$ . If $11\,\alpha(10, 6) + 18\,\alpha(11, 5) = p\,(14)^6$ , then $p$ is equal…HardNumerical value
2 Apr 2017 (offline) · Q74Let $I_n=\int\tan^n x\,dx,\ (n>1)$ . If $I_4+I_6=a\tan^5x+bx^5+C$ , where C is a constant of integration, then the ordered pair (a, b) is…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.