JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 June 2022, Shift 1, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

\int \frac{(x^2+1)e^x}{(x+1)^2}\,dx = f(x)e^x+C

, where C is a constant, then

\frac{d^3f}{dx^3}

x=1

is equal to :

(1) $-\frac{3}{4}$
(2) $\frac{3}{4}$ Official answer
(3) $-\frac{3}{2}$
(4) $\frac{3}{2}$

Official answer

Option 2

NTA final key.

Chapter: Integrals
Topic: Integration by Parts
Idea tested: Exponential Form with Improper Rational Functions

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
4 Apr 2024, Shift 2 · Q26If…HardNumerical value
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
6 Apr 2023, Shift 1 · Q11Let $I(x)=\int\frac{x^2(x\sec^2x+\tan x)}{(x\tan x+1)^2}\,dx$ . If $I(0)=0$ , then $I\left(\frac{\pi}{4}\right)$ is equal toHardSingle 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

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.