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Saturday, 31 October

JEE Main · Maths · Integrals

Exponential Form with Improper Rational Functions

JEE Main asked Exponential Form with Improper Rational Functions once in the 108 shifts Lumi analysed, on 27 Jun 2022, Shift 1. It belongs to Integration by Parts, in Integrals (Maths).

Updated 2026-10-24

Times asked
1
in 1 shift
Years
1 of 8
First asked
2022
the only year
Pattern
Occasional
asked once so far

Questions on this idea a shift, by year

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

00.050.10’170’200’210.04’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 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
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20221 of 24
  • 20210 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Integral of exponential form then higher derivative

Difficulty

Easy 0Medium 1Hard 0

The question was multiple choice.

Every question

The question

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

  1. 27 Jun 2022, Shift 1 · Q9If ∫(x2+1)ex(x+1)2 dx=f(x)ex+C\int \frac{(x^2+1)e^x}{(x+1)^2}\,dx = f(x)e^x+C, where C is a constant, then d3fdx3\frac{d^3f}{dx^3} at x=1x=1 is equal to :MediumSingle correct

Shift: 27 Jun 2022, Shift 1.

Same topic

Other ideas in Integration by Parts

Integration by Parts has 9 ideas JEE Main has asked; 4 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas