Indefinite Integration JEE Main PYQs PDF, 2020–2026

Indefinite Integration has 60 questions in JEE Main papers from 2020 to 2026, about 8.6 per year across all shifts. All 60 are in the free PDF, with an answer key. The most asked topic is Integration by Substitution (39 questions), followed by Standard Integrals (9) and Integration by Parts (7).

Asked in JEE Main: 602020–2026, all shifts
In this free PDF: 60all of them, with answers
Asked in 2026: 7Latest paper: 2026 Apr S2
Most asked topic: Integration by Substitution39 Qs · 65% of the chapter
Difficulty mix: 1% easy · 67% medium · 32% hardof the questions in the PDF

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Source: official NTA JEE Main papers · Updated 25 Oct 2026

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1 of this chapter's questions came back in a later paper (2021–2026). See the most repeated.

How often it's asked in JEE Main

Indefinite Integration had about 0.4 questions per shift in recent JEE Main papers (2024–26). Most asked topic: Integration by Substitution. About 7 questions in the 2026 papers.

It came up in about 23 of the 2024–26 shifts in our bank. Question types in 2020–2026: about 44 MCQs and about 16 numerical.

How many questions from Indefinite Integration in JEE Main, year by year

Year	Questions	Per shift	MCQ	Numerical
2026	7	0.4	6	1
2025	8	0.4	5	3
2024	8	0.4	6	2
2023	10	0.4	7	3
2022	7	0.3	6	1
2021	11	0.4	5	6
2020	9	0.6	9	0
2020–2026	60	0.4	44	16

Most asked Indefinite Integration topics, 2020–2026

Topic	Questions
Integration by Substitution	39
Standard Integrals	9
Integration by Parts	7
Partial Fractions	5

Counted from PrepWiser's question bank of JEE Main papers, 2020–2026. Per shift = questions that year ÷ shifts in our bank. Updated 25 Oct 2026.

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Two free sheets, made from the past JEE Main questions on this chapter.

Revision notes7 pages, 22 ideas with the usual mistakes.Open the revision notes Formula sheet3 pages, all 26 formulas.Open the formula sheet

Indefinite Integration questions per year

Year	Asked	In PDF
2026	7	7
2025	8	8
2024	8	8
2023	10	10
2022	7	7
2021	11	11
2020	9	9

Topic-wise weightage by year

How many Indefinite Integration questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Topic	Asked	Share	2026	2025	2024	2023	2022	2021	2020
Integration by Substitution	39	65%	5	5	6	5	3	8	7
Standard Integrals	9	15%	·	1	1	3	2	·	2
Integration by Parts	7	12%	·	2	1	2	2	·	·
Partial Fractions	5	8%	2	·	·	·	·	3	·
All topics	60	100%	7	8	8	10	7	11	9

Swipe the table sideways for older years.

Newest questions (2026)

All 7 JEE Main 2026 Indefinite Integration questions in the free PDF, latest shift first.

JEE Main 2026 · 2 Apr · Shift 2 · Partial Fractions

Let $f(x)=\int \left(\frac{16x+24}{x^{2}+2x-15}\right)dx$ . If $f(4)=14\log_{e}(3)$ and $f(7)=\log_{e}(2^{\alpha}\cdot 3^{\beta})$ , $\alpha,\beta\in {\mathbb{N}}$ , then $\alpha+\beta$ is equal to :
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JEE Main 2026 · 28 Jan · Shift 1 · Integration by Substitution

If $\int \left(\frac{1-5\cos^{2}x}{\sin^{5}x\cos^{2}x}\right)dx=f(x)+{\mathrm{C}}$ , where C is the constant of integration, then $f\left(\frac{\pi}{6}\right)-f\left(\frac{\pi}{4}\right)$ is equal to

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JEE Main 2026 · 28 Jan · Shift 2 · Partial Fractions

Let $f(x)=\int \frac{dx}{x^{{2/3}}+2x^{{1/2}}},$ be such that $f(0)=-26+24\log_{e}(2)$ . If $f(1)=a+b\log_{e}(3)$ , where $a,b\in {\mathbb{Z}}$ , then $a+b$ is equal to :
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JEE Main 2026 · 24 Jan · Shift 1 · Integration by Substitution

Let $f(t)=\int \left(\frac{1-\sin (\log_{e}t)}{1-\cos (\log_{e}t)}\right)dt,t>1$ .

If $f\left(e^{{\pi/2}}\right)=-e^{{\pi/2}}$ and $f\left(e^{{\pi/4}}\right)=\alpha e^{{\pi/4}}$ , then $\alpha$ equals

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JEE Main 2026 · 23 Jan · Shift 1 · Integration by Substitution

Let $f(x)=\int \frac{\left(2-x^{2}\right)\cdot {\mathrm{e}}^{x}}{(\sqrt{1+x})(1-x)^{{3/2}}}{\ \mathrm{d}}x$ . If $f(0)=0$ , then $f\left(\frac{1}{2}\right)$ is equal to:

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JEE Main 2026 · 23 Jan · Shift 2 · Integration by Substitution

Let ${\mathrm{I}}(x)=\int \frac{3dx}{(4x+6)\left(\sqrt{4x^{2}+8x+3}\right)}$ and ${\mathrm{I}}(0)=\frac{\sqrt{3}}{4}+20$ . If

${\mathrm{I}}\left(\frac{1}{2}\right)=\frac{a\sqrt{2}}{b}+{\mathrm{c}}$ , where $a,b,{\mathrm{c}}\in {\mathrm{N}},\gcd (a,b)=1$ , then $a+b+c$ is equal to :

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JEE Main 2026 · 22 Jan · Shift 1 · Integration by Substitution

If $\int (\sin x)^{{\frac{-11}{2}}}(\cos x)^{{\frac{-5}{2}}}dx=-\frac{p_{1}}{q_{1}}(\cot x)^{{\frac{9}{2}}}-\frac{p_{2}}{q_{2}}(\cot x)^{{\frac{5}{2}}}-\frac{p_{3}}{q_{3}}(\cot x)^{{\frac{1}{2}}}+\frac{p_{4}}{q_{4}}(\cot x)^{{\frac{-3}{2}}}+{\mathrm{C}}$ , where $p_{i}$ and $q_{i}$ are positive integers with $\gcd (p_{i},q_{i})=1$ for $i=1,2,3,4$ and C is the constant of integration, then $\frac{15p_{1}p_{2}p_{3}p_{4}}{q_{1}q_{2}q_{3}q_{4}}$ is equal to $\_\_\_\_$
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Sample questions from recent papers

JEE Main 2025 · 23 Jan · Shift 1 · Standard Integrals

Let ${\mathrm{I}}(x)=\int \frac{dx}{(x-11)^{{\frac{11}{13}}}(x+15)^{{\frac{15}{13}}}}$ . If ${\mathrm{I}}(37)-{\mathrm{I}}(24)=\frac{1}{4}\left(\frac{1}{{\ \mathrm{b}}^{{\frac{1}{13}}}}-\frac{1}{{\mathrm{c}}^{{\frac{1}{13}}}}\right),{\mathrm{b}},{\mathrm{c}}\in {\mathcal{N}}$ , then $3({\ \mathrm{b}}+{\mathrm{c}})$ is equal to

(A)39
(B)22
(C)40
(D)26

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Answer: (A)

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JEE Main 2025 · 23 Jan · Shift 2 · Integration by Parts

Let $\int x^{3}\sin x{\ \mathrm{d}}x=g(x)+C$ , where $C$ is the constant of integration. If $8\left(g\left(\frac{\pi}{2}\right)+g^{{'}}\left(\frac{\pi}{2}\right)\right)=\alpha\pi^{3}+\beta\pi^{2}+\gamma,\alpha,\beta,\gamma\in Z$ , then $\alpha+\beta-\gamma$ equals :

(A)47
(B)55
(C)62
(D)48

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Answer: (B)

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JEE Main 2021 · 31 Aug · Shift 2 · Partial Fractions

\int {{\frac{{\sin x}}{{{{\sin}^{3}}x+{{\cos}^{3}}x}}}dx=}

\alpha{\log_{e}}|1+\tan x|+\beta{\log_{e}}|1-\tan x+{\tan^{2}}x|+\gamma{\tan^{{-1}}}\left({{\frac{{2\tan x-1}}{{\sqrt{3}}}}}\right)+C

, when C is constant of integration, then the value of

18(\alpha+\beta+{\gamma^{2}})

is ______________.

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Answer: 3

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Frequently asked

How many questions come from Indefinite Integration in JEE Main?

60 questions from 2020 to 2026, about 8.6 per year. In 2026 it had 7.

Which Indefinite Integration topics are most important for JEE Main?

By past papers: Integration by Substitution (65%), Standard Integrals (15%) and Integration by Parts (12%) of all Indefinite Integration questions.

Is the Indefinite Integration PYQ PDF free?

Yes. The PDF and its answer key are free, and you can practise the questions online with no login, with step-by-step solutions where available.

Prefer to solve online? Practise Indefinite Integration online with step-by-step solutions where available, or work through JEE Main papers shift by shift.

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JEE Main PYQs by year: 2026 · 2025 · 2024 · 2023 · 2022 · 2021 · 2020

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Indefinite Integration JEE Main PYQs PDF, 2020–2026

How often it's asked in JEE Main

How many questions from Indefinite Integration in JEE Main, year by year

Most asked Indefinite Integration topics, 2020–2026

Revise Indefinite Integration before you practise

Send this chapter to your study group

Indefinite Integration questions per year

Topic-wise weightage by year

Newest questions (2026)

Sample questions from recent papers

Practise these online, free, no login

Frequently asked

How many questions come from Indefinite Integration in JEE Main?

Which Indefinite Integration topics are most important for JEE Main?

Is the Indefinite Integration PYQ PDF free?

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