Indefinite Integration

42 NDA Mathematics previous year questions (PYQs) from 17 papers, 2017 to 2026, with answers and worked solutions.

About this chapter

Difficulty: 6 easy · 27 moderate · 9 hard.
Most-asked subtopics: Integration by Substitution — Algebraic, Trigonometric, and Composite Forms (18), Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals (14), Integration by Partial Fractions (7).
Updated 14 September 2026.

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NDA · Sep 2026 · Q73Moderate
#1Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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NDA · Apr 2017 · Q85Moderate
#2Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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NDA · Sep 2018 · Q84Easy
#3Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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NDA · Apr 2019 · Q94Easy
#4Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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NDA · Sep 2019 · Q81Moderate
#5Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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NDA · Apr 2020 · Q78Moderate
#6Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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NDA · Apr 2020 · Q90Easy
#7Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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NDA · Apr 2021 · Q100Moderate
#8Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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NDA · Apr 2022 · Q63Moderate
#9Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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NDA · Sep 2022 · Q75Moderate
#10Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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Set · 2 questions
For the following two (02) items: Let $u=\int e^x\cos x\,dx$ and $v=\int e^x\sin x\,dx$ .
- NDA · Sep 2025 · Q85Moderate
  #11Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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- NDA · Sep 2025 · Q86Hard
  #12Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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Set · 2 questions
Let $2\displaystyle\int\dfrac{x^2-1}{\sqrt{x^2+1}}\,dx = U(x)V(x)-3\ln\{U(x)+V(x)\}+c$ .
- NDA · Sep 2024 · Q99Hard
  #13Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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- NDA · Sep 2024 · Q100Hard
  #14Standard Forms — Exponential, Logarithmic, and Paired Trigonometric Integrals
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NDA · Sep 2026 · Q71Moderate
#15Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Apr 2017 · Q76Moderate
#16Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Sep 2017 · Q67Moderate
#17Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Apr 2018 · Q90Hard
#18Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Sep 2018 · Q83Easy
#19Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Sep 2018 · Q97Moderate
#20Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Sep 2019 · Q82Moderate
#21Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Apr 2021 · Q85Hard
#22Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Apr 2021 · Q86Easy
#23Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Sep 2021 · Q81Moderate
#24Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Sep 2021 · Q85Moderate
#25Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Apr 2022 · Q62Moderate
#26Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Sep 2022 · Q74Hard
#27Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Sep 2022 · Q76Hard
#28Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Sep 2025 · Q95Moderate
#29Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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Set · 2 questions
Let $\displaystyle\int\dfrac{dx}{\sqrt{x+1}-\sqrt{x-1}}=\alpha(x+1)^{3/2}+\beta(x-1)^{3/2}+c$ .
- NDA · Apr 2024 · Q95Moderate
  #30Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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- NDA · Apr 2024 · Q96Moderate
  #31Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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Set · 1 question
Let the function $y = (1 - \cos x)^{-1}$ , where $x \neq 2n\pi$ and $n$ is an integer.
- NDA · Apr 2025 · Q82Moderate
  #32Integration by Substitution — Algebraic, Trigonometric, and Composite Forms
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NDA · Sep 2017 · Q88Moderate
#33Integration by Parts
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NDA · Apr 2019 · Q87Moderate
#34Integration by Parts
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NDA · Apr 2020 · Q83Moderate
#35Integration by Parts
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NDA · Apr 2017 · Q73Moderate
#36Integration by Partial Fractions
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NDA · Apr 2020 · Q88Moderate
#37Integration by Partial Fractions
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NDA · Sep 2021 · Q93Moderate
#38Integration by Partial Fractions
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Set · 2 questions
For the next two (02) items that follow: Let $\int\dfrac{\sin\theta\,d\theta}{(2+\cos\theta)(3+4\cos\theta)}=A\ln|2+\cos\theta|+B\ln|3+4\cos\theta|$ .
- NDA · Apr 2026 · Q91Hard
  #39Integration by Partial Fractions
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- NDA · Apr 2026 · Q92Hard
  #40Integration by Partial Fractions
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Set · 2 questions
Given that $\displaystyle\int\dfrac{3\cos x+4\sin x}{2\cos x+5\sin x}\,dx=\dfrac{\alpha x}{29}+\dfrac{\beta}{29}\ln|2\cos x+5\sin x|+c$ .
- NDA · Apr 2024 · Q81Moderate
  #41Integration by Partial Fractions
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- NDA · Apr 2024 · Q82Easy
  #42Integration by Partial Fractions
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Indefinite Integration

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