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Mathematics - Indefinite Integration

Practise 105 JEE Main previous year questions on Indefinite Integration, compiled from papers spanning 2004 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Main tests.

Indefinite Integration has been asked in 19 of the 25 years of JEE Main papers analysed (2002–2026), with 105 questions in all. 6% of them were easy, 53% moderate and 41% tough. Most of its questions came from 2019, with 16 questions that year. In the last three years (2024–2026) it had 20 questions across 49 papers, about 0.4 per paper.

The chapter's 4 topics are not weighted equally: Integration by Substitution (75 questions, 71%), Integration by Parts (16 questions, 15%), and Miscellaneous Forms (11 questions, 10%) have been asked the most. Integration by Substitution has also led over the last five years, with 23 questions. Integration by Substitution has produced the most tough questions (31).

  1. 1Let . If and , , then is equal to:02 Apr, 2026 (E)Integration by Substitution
  2. 2Let be such that . If , where , then is equal to :28 Jan, 2026 (E)Integration by Substitution
  3. 3Let . If and , then equals24 Jan, 2026 (M)Integration by Parts
  4. 4Let . If , then is equal to:23 Jan, 2026 (M)Integration by Parts
  5. 5Let and . If , where , then is equal to23 Jan, 2026 (E)Integration by Substitution
  6. 6If , where and are positive integers with for and C is the constant of integration, then is equal to22 Jan, 2026 (M)Integration by Substitution
  7. 7If , where is the constant of integration, then is equal to ________ .07 Apr, 2025 (E)Integration by Substitution
  8. 8If is the constant of integration and , then is equal to04 Apr, 2025 (E)Integration by Substitution
  9. 9Let . If , then is equal to03 Apr, 2025 (M)Integration by Substitution
  10. 10If , then is equal to :28 Jan, 2025 (E)Integration using Partial Fraction
  11. 11If , where is the constant of integration, then is equal to _______.24 Jan, 2025 (E)Integration by Substitution
  12. 12Let . If , then is equal to23 Jan, 2025 (M)Miscellaneous Forms
  13. 13Let , where is the constant of integration. If , then equals :23 Jan, 2025 (E)Integration by Parts
  14. 14If , where C is the constant of integration, then equals :22 Jan, 2025 (E)Integration by Parts
  15. 15Let , where is the constant of integration. Then is equal to :09 Apr, 2024 (M)Integration by Substitution
  16. 16Let . If , then is equal to08 Apr, 2024 (M)Integration by Substitution
  17. 17If , where is the constant of integration, then the value of is__________08 Apr, 2024 (E)Integration by Substitution
  18. 18If constant, then the maximum value of , is :06 Apr, 2024 (E)Integration by Substitution
  19. 19If where and is the constant of integration, then the value of equals _______04 Apr, 2024 (E)Integration by Substitution
  20. 20If ∫ sin 3 2 x + cos 3 2 x sin 3 x cos 3 x sin ( x - θ ) d x = A cos θ tan x - sin θ + B cos θ - sin θ cot x + C , where C is the integratio29 Jan, 2024 (E)Integration by Substitution
  21. 21The integral ∫ x 8 - x 2 dx x 12 + 3 x 6 + 1 tan - 1 x 3 + 1 x 3 is equal to :27 Jan, 2024 (E)Integration by Substitution
  22. 22Let f x = d x 3 + 4 x 2 4 - 3 x 2 , x 2 3 . If f 0 = 0 and f 1 = 1 tan - 1 , , 0 , then 2 + 2 is equal to _______.15 Apr, 2023 (M)Integration by Substitution
  23. 230 6 e 3 x + 6 e 2 x + 11 e x + 6 d x =13 Apr, 2023 (M)Integration using Partial Fraction
  24. 24Let I x = x + 7 x d x and I 9 = 12 + 7 log e 7 . If I 1 = + 7 log e 1 + 2 2 , then 4 is equal to _____.12 Apr, 2023 (M)Integration by Substitution
  25. 25If I x = e sin 2 x cos x sin 2 x - sin x d x and I 0 = 1 , then I 3 is equal to10 Apr, 2023 (M)Integration by Parts
  26. 26For , , , , if x e 2 x + e x 2 x log e x d x = 1 x e x - 1 e x x + C , where e = n = 0 1 n ! and C is constant of integration, then + 2 + 3 10 Apr, 2023 (E)Integration by Substitution
  27. 27Let I x = x + 1 x 1 + x e x 2 d x , x 0 . If lim x I x = 0 then I 1 is equal to08 Apr, 2023 (M)Integration by Substitution
  28. 28The integral x 2 x + 2 x x log 2 x d x is equal to08 Apr, 2023 (E)Integration by Substitution
  29. 29Let I x = x 2 x sec 2 + tan x ( x tan x + 1 ) 2 d x If I 0 = 0 , then I 4 is equal to06 Apr, 2023 (M)Integration by Parts
  30. 30If sec 2 x - 1 d x = log e cos 2 x + + cos 2 x 1 + cos 1 x + constant, then - is equal to ______.30 Jan, 2023 (E)Integration by Substitution
  31. 31Let f x = 2 x x 2 + 1 x 2 + 3 d x . If f 3 = 1 2 log e 5 - log e 6 , then f 4 is equal to25 Jan, 2023 (M)Integration using Partial Fraction
  32. 32For I x = sec 2 x - 2022 sin 2022 x d x , if I 4 = 2 1011 , then29 Jul, 2022 (E)Integration by Parts
  33. 33The integral 1 - 1 3 cos x - sin x 1 + 2 3 sin 2 x d x is equal to26 Jul, 2022 (E)Integration by Substitution
  34. 34x 2 + 1 e x x + 1 2 d x = f x e x + C , where C is a constant, then d 3 f d x 3 at x = 1 is equal to27 Jun, 2022 (M)Integration by Parts
  35. 35If 1 x 1 - x 1 + x d x = g x + c , g 1 = 0 , then g 1 2 is equal to26 Jun, 2022 (E)Integration by Substitution
  36. 36Let g : 0 , R be a differentiable function such that x cos x - sin x e x + 1 + g x e x + 1 - x e x e x + 1 2 d x = x g x e x + 1 + C , for a25 Jun, 2022 (M)Integration by Parts
  37. 37The integral 1 ( x - 1 ) 3 ( x + 2 ) 5 4 d x is equal to : (where C is a constant of integration)31 Aug, 2021 (M)Integration by Substitution
  38. 38If sin x sin 3 x + cos 3 x d x = log e | 1 + tan x | + log e 1 - tan x + tan 2 x + tan - 1 2 tan x - 1 3 + C , when C is constant of integra31 Aug, 2021 (E)Integration by Substitution
  39. 39If d x x 2 + x + 1 2 = a tan - 1 2 x + 1 3 + b 2 x + 1 x 2 + x + 1 + C , x 0 where C is the constant of integration, then the value of 9 ( 327 Aug, 2021 (M)Integration by Substitution
  40. 402 e x + 3 e - x 4 e x + 7 e - x d x = 1 14 u x + v log e 4 e x + 7 e - x + C , where C is a constant of integration, then u + v is equal to27 Aug, 2021 (E)Integration by Substitution
  41. 41The integral ( 2 x - 1 ) cos ( 2 x - 1 ) 2 + 5 4 x 2 - 4 x + 6 d x is equal to (where c is a constant of integration)18 Mar, 2021 (M)Integration by Substitution
  42. 42If f x = 5 x 8 + 7 x 6 x 2 + 1 + 2 x 7 2 d x , x 0 , f 0 = 0 and f 1 = 1 K , then the value of K is18 Mar, 2021 (M)Integration by Substitution
  43. 43For real numbers , , and , if x 2 - 1 + tan - 1 x 2 + 1 x x 4 + 3 x 2 + 1 tan - 1 x 2 + 1 x d x = log e tan - 1 x 2 + 1 x + tan - 1 x 2 - 1 16 Mar, 2021 (E)Integration by Substitution
  44. 44The value of the integral sin sin 2 sin 6 + sin 4 + sin 2 2 sin 4 + 3 sin 2 + 6 1 - cos 2 d is (where c is a constant of integration)25 Feb, 2021 (M)Integration by Substitution
  45. 45The integral e 3 log e 2 x + 5 e 2 log e 2 x e 4 log e x + 5 e 3 log e x - 7 e 2 log e x d x , x 0 , is equal to (where c is a constant of i25 Feb, 2021 (E)Integration by Substitution
  46. 46If cos x - sin x 8 - sin 2 x d x = a sin - 1 sin x + cos x b + c , where c is a constant of integration, then the ordered pair a , b is equa24 Feb, 2021 (M)Integration by Substitution
  47. 47If I 1 = 0 1 1 - x 50 100 d x and I 2 = 0 1 1 - x 50 101 d x such that I 2 = I 1 then equals to :06 Sep, 2020 (M)Integration by Parts
  48. 48If e 2 x + 2 e x - e - x - 1 e e x + e - x d x = g ( x ) e e x + e - x + c , where c is a constant of integration, then g ( 0 ) is05 Sep, 2020 (M)Integration by Parts
  49. 49If cos 5 + 7 sin - 2 cos 2 d = Alog e | B ( ) | + C , where C is a constant of integration, then B ( ) A can be:05 Sep, 2020 (E)Integration by Substitution
  50. 50The integral x x sin x + cos x 2 d x is equal to, (where C is a constant of integration):04 Sep, 2020 (M)Integration by Substitution

Frequently Asked Questions

1.How many questions are available for Indefinite Integration?

This chapter includes 105 questions compiled from JEE Main papers spanning 2004 to 2026.

2.Are these questions only from JEE Main, or from other exams too?

These are JEE Main questions specifically for the Indefinite Integration chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Indefinite Integration an important chapter for JEE Main Mathematics?

Indefinite Integration has appeared in 19 of the 25 years of JEE Main papers covered here, with 105 questions across 102 papers - about one per paper it appears in.

4.What is the difficulty level of Indefinite Integration questions in JEE Main?

Of the 105 questions analysed for this chapter, 6% are easy, 53% moderate and 41% tough. 2019 had the most, with 16 questions.

5.Which topics in Indefinite Integration should I focus on?

These topics have carried the most weightage in Indefinite Integration:

  • Integration by Substitution - 75 questions (71%)
  • Integration by Parts - 16 questions (15%)
  • Miscellaneous Forms - 11 questions (10%)
  • Integration by Substitution has produced the most tough questions (31).
6.Is Indefinite Integration's weightage in JEE Main going up or down?

Across all 102 papers analysed, Indefinite Integration has averaged about 1.0 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.4 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.