JEE Main Maths · Integrals

Integration by Parts in JEE Main

Name: Integration by Parts: JEE Main previous year questions
Creator: Lumi

Integration by Parts (Maths, Integrals) came 6 times in 5 of the 42 JEE Main shifts Lumi analysed, across 5 distinct ideas. 2 of them came in 2024–26; it was last asked in 2025.

Questions: 6; in 5 shifts
Ideas asked: 5; 1 asked more than once
Numerical answer: 1; 17% of its questions
Pattern: Frequent; last asked 2025

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 0Medium 2Hard 4

Format

Single correct5 Q
Numerical value1 Q

Ideas inside the topic

5 ideas

Logarithm of Quadratic Roots2 Q
Generalized Reverse Product Rule1 Q
Algebraic Reduction Formulas1 Q
Trigonometric Reduction Formulas1 Q
Roots of Quadratics via Parts1 Q

Where it sits

Part of Integrals, which had 73 questions in all. Integration by Parts accounts for 8% of them. In Lumi's JEE taxonomy it belongs to Calculus.

Every question

All 6 Integration by Parts questions

Newest first, each with its options and official answer.

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
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
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