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Saturday, 31 October

JEE Main · Maths · Integrals

Factoring Highest Power for Substitution

JEE Main asked Factoring Highest Power for Substitution 3 times in 3 of the 108 shifts Lumi analysed, in 2020, 2022 and 2025. It belongs to Integration by Substitution, in Integrals (Maths). The longest wait between two years asking it was 3 years.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
3 of 8
First asked
2020
last in 2025
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2022 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.08’200’210.04’220’230’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 1 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20251 of 8
  • 20240 of 18
  • 20230 of 12
  • 20221 of 24
  • 20210 of 24
  • 20201 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: multi-step.

  • Integrate algebraic radical expression by substitution
  • Integral by factoring out highest power

Difficulty

Easy 0Medium 0Hard 3

2 of the 3 questions had a numerical answer.

Every question

All 3 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 7 Apr 2025, Shift 2 · Q24If…HardNumerical value
  2. 26 Jun 2022, Shift 2 · Q28The integral 24π∫02(2−x2) dx(2+x2)4+x4\frac{24}{\pi}\int_0^{\sqrt{2}} \frac{(2 - x^2)\,dx}{(2 + x^2)\sqrt{4 + x^4}} is equal to ______.HardNumerical value
  3. 8 Jan 2020, Shift 1 · Q60If ∫cos⁡x dxsin⁡3x (1+sin⁡6x)2/3=f(x) (1+sin⁡6x)1/λ+c\int\dfrac{\cos x\,dx}{\sin^3 x\,(1+\sin^6 x)^{2/3}}=f(x)\,(1+\sin^6 x)^{1/\lambda}+c where c is a constant of integration, then…HardSingle correct

Shifts: 8 Jan 2020, Shift 1, 26 Jun 2022, Shift 2, 7 Apr 2025, Shift 2.

Same topic

Other ideas in Integration by Substitution

Integration by Substitution has 27 ideas JEE Main has asked; 12 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas