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Mathematics - Indefinite Integration

Practise 104 NTA Abhyas (JEE Main) questions on Indefinite Integration. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Indefinite Integration has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 104 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1The value of the integral e x 2 + 1 x 2 x 2 - 1 x + 1 d x is equal to (where C is the constant of integration)
  2. 2The integral I = 2 sin x 3 + sin 2 x d x simplifies to (where, C is the constant of integration)
  3. 3The value of the integral Ι = ∫ d x 1 + s i n x , ∀ x ∈ 0 , π 2 is equal to k ln ⁡ t a n π 4 + x 8 + c , then the value of k 2 is equal to (
  4. 4If the integral I = x x - 3 x + 3 x - 1 x - 2 x + 1 d x = f x + C (where, x 0 and C is the constant of integration) and f 1 = - 1 3 , then t
  5. 5If I = dx x 2 1 + x 2 = f x x + C , x 0 (where, C is the constant of integration) and f 1 = - 2 , then the value of f 3 is
  6. 6The value of the integral = e x sin x + cos x d x is equal to e x f x + C , C being the constant of integration. Then the maximum value of y
  7. 7The value of the integral sin x x 6 x c o s x - sin x x 2 d x is (where, c is an arbitrary constant)
  8. 8Consider the integrals I = sin x 3 cos x + 4 sin x d x and J = cos x 3 cos x + 4 sin x d x . Then, the integral 4 J - 3 I is equal to (where
  9. 9If I = 1 + x 4 1 - x 4 3 2 d x = 1 f x + C (where, C is the constant of integration) and f 2 = - 15 4 , then the value of 2 f 1 2 is
  10. 10If the integral Ι = ∫ x s i n x c o s x ⋅ ln ⁡ x + s i n x x dx = f x g x + c ∀ x 0 , then the range of y = g x is (where, c is an arbitrary
  11. 11If ∫ d x e x - 1 = 2 t a n - 1 f x + C , (where x 0 and C is the constant of integration) then the range of f x is
  12. 12The value of ∫ d x x ( x n + 1 ) is equal to
  13. 13Let f x = 2 x + 1 and g x = f x x 2 x + 1 2 d x . If 6 g 2 + 1 = 0 , then g - 1 2 is equal to
  14. 14Let x 3 + x 2 + x 12 x 3 + 15 x 2 + 20 x d x = f x where f 1 = 47 30 . If f 2 2 is equal to p 225 , then the value of p is equal to
  15. 15The least value of n n N , such that the function f n , x = n cos n x d x satisfies f n , 2 = - 1 , is (given, f n , 0 = 0 )
  16. 16If Ι = ∫ t a n - 1 e x e x + e - x d x = t a n - 1 f x 2 2 + C (where C is the constant of integration), then the range of y = f x ∀ x ∈ R i
  17. 17The value of ∫ x d x ( x + 3 ) x + 1 is (where, c is the constant of integration)
  18. 18The value of e x x 1 + e 2 x d x is equal to (where, C is the constant of integration)
  19. 19If m is any natural number, then the value of the integral ∫ x 3 m + x 2 m + x m 2 x 2 m + 3 x m + 6 1 / m dx is (where, C is an arbitrary c
  20. 20The value of cos x sin 2 x sin x + cos x d x is equal to
  21. 21If x p q - p - 1 x p + 1 q d x = 2 ( 1+ x - p ) 1 - q p ( q - 1 ) + c p , q N - { 1 } , then the value of is (here, c is an arbitrary consta
  22. 22The indefinite integral I = ∫ sin 2 ⁡ x - cos 2 ⁡ x 2019 sin ⁡ x 2021 cos ⁡ x 2021 d x simplifies to (where c is an integration constant)
  23. 23Consider the integrals I 1 = ∫ e x 2 cos ⁡ x d x and I 2 = ∫ x e x 2 sin ⁡ x d x . Then, I 1 + 2 I 2 simplifies to (where, c is the constant
  24. 24The value of the ∫ s i n 8 x - c o s 8 x 1 - 2 s i n 2 x c o s 2 x d x is equal to (where, C is the constant of integration)
  25. 25If the integral I = x 5 1 + x 3 d x = K x 3 + 1 x 3 - 2 + C , (where, C is the constant of integration), then the value of 9 K is equal to
  26. 26Let I = d x cos x - sin x 2 = 1 f x + C (where, C is the constant of integration). If f 3 = 1 - 3 , then the number of solution(s) of f x =
  27. 27If I = ∫ x 3 - 1 x 5 + x 4 + x + 1 d x = 1 4 ln ⁡ f x - ln ⁡ g x + c (where, c is the constant of integration) and f 0 = g 0 = 1 , then the
  28. 28The value of x - 4 x 2 x - 2 d x is equal to (where, C is the constant of integration)
  29. 29The value of the integral ∫ e 3 s i n - 1 x 1 1 - x 2 + e 3 c o s - 1 x d x is equal to (where, c is an arbitrary constant)
  30. 30Let sin 2 x ln ( cos x ) d x = f ( x ) cos 2 x + C , (where, C is the constant of integration) and f 0 = 1 2 . If f 3 is equal to 1 a + ln b
  31. 31The integral ∫ x cos - 1 1 - x 2 1 + x 2 dx ; x 0 is equal to
  32. 32The value of sin 101 x . sin 99 x d x is sin 100 x sin 100 x k + 5 , then k 19 is
  33. 33If the integral = e x 2 x 3 d x = e x 2 f x + c , where c is the constant of integration and f 1 = 0 , then the value of f 2 is equal to
  34. 34Let ∫ 1 - ln ⁡ x x 2 d x = f x , for all positive x . If f e = 1 e , then f 2 + f 4 is equal to
  35. 35The graph of the antiderivative of f x = x e x 2 passes through 0 , 3 , then the value of g 2 - f 0 is
  36. 36Let the integral I = 2020 x + sin - 1 2020 x 1 - 2020 2 x d x = K 2 2020 sin - 1 2020 x + (where, is the constant of integration), then the
  37. 37∫ sin 8 x − cos 8 x 1 − 2 sin 2 x cos 2 x dx is equal to (where C is an arbitrary constant)
  38. 38Consider 3 x 4 + 2 x 2 + 1 x 4 + x 2 + 1 d x = f x . If f 1 = 3 , then f 2 2 is equal to
  39. 39The integral I = ∫ sin 3 ⁡ θ cos ⁡ θ 1 + sin 2 ⁡ θ 2 d θ simplifies to (where, c is the constant of integration)
  40. 40If B = 1 e x + 1 d x = - f ( x ) + C , where, C is the constant of integration and e f 0 = 2 , then the value of e f - 1 is
  41. 41The value of the integral d x 1 + x x - x 2 is equal to (where, C is the constant of integration)
  42. 42The value of the integral x 1 3 1 - x 3 d x is equal to (where c is the constant of integration)
  43. 43The integral = s i n x 2 + 2 x 2 c o s x 2 d x = x H x + C , (where C is the constant of integration). If the range of H ( x ) is a , b , th
  44. 44Let A n = tan n x d x , n N . If A 10 + A 12 = tan m x m + (where is an arbitrary constant), then the value of m is equal to
  45. 45The integral = e x 1 + sin x 1 + cos x d x = e x f x + C (where, C is the constant of integration). Then, the range of y = f x (for all x in
  46. 46The integral I = sec 3 x tan 3 x d x is equal to (where, C is the constant of integration)
  47. 47The integral I = ∫ e x cos ⁡ e x x d x = f x + c (where, c is the constant of integration) and f ln ⁡ π 4 2 = 2 . Then, the number of soluti
  48. 48Let f n , x = n c o s n x d x , with f n , 0 = 0 . If the expression x = 1 89 f 1 , x simplifies to sin a sin b sin c , then the value of b
  49. 49The value of the integral c o s e c 2 x - 2019 c o s 2019 x d x is equal to (where C is the constant of integration)
  50. 50If I n = ln x n d x , then I 10 + 10 I 9 is equal to (where C is the constant of integration)

Frequently Asked Questions

1.How many questions are available for Indefinite Integration?

This chapter includes 104 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Indefinite Integration questions in NTA Abhyas (JEE Main)?

Of the 104 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

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

All of this chapter's questions come from a single topic: Uncategorized.