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JEE Indefinite Integration PYQs with Solutions

297 previous year questions from Indefinite Integration (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

297 questionsMathematics2004–2026Answers + solutions

About Indefinite Integration PYQs

Indefinite Integration has 297 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (104), NTA Abhyas JEE Main (104), 99 Percentile Qs Bank for JEE Main (7) and 1 other source, spanning 2004 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 6
  • 2025: 8
  • 2024: 7
  • 2023: 10
  • 2022: 5
  • 2021: 10
  • 2020: 113
  • 2019: 16
  • 2018: 5
  • 2017: 3
  • 2016: 3
  • 2015: 3

Indefinite Integration questions with solutions

1

Let f(x) = ∫ ((16x + 24)/(x^2 + 2x - 15)) dx . If f(4) = 14 _e(3) and f(7) = _e(2^ α · 3^ β ) , α, β ∈ ℕ , then α + β is equal to:

JEE Main 2026 Solution View → 2

Let f(x)=∫ d x x^ ((2)/(3)) +2 x^ ((1)/(2)) be such that f(0)=-26+24 _ e (2) . If f(1)=a+b _ e (3) , where a, b ∈ Z , then a+b is equal to :

JEE Main 2026 Solution View → 3

Let f(t)=∫( 1- ( _ e t) 1- ( _ e t) ) d t, t>1 . If f(e^ π / 2 )=-e^ π / 2 and f(e^ π / 4 )=α e^ π / 4 , then α equals

JEE Main 2026 Solution View → 4

Let I(x)=∫ 3 d x (4 x+6)( 4 x^ 2 +8 x+3 ) and I(0)= 3 4 +20 . If I((1)/(2))= a 2 b +c , where a, b, c ∈ N, gcd(a, b)=1 , then a+b+c is equal to

JEE Main 2026 Solution View → 5

Let f(x)=∫ (2-x^ 2 ) · e^ x ( 1+x )(1-x)^ 3 / 2 ~d x . If f(0)=0 , then f((1)/(2)) is equal to:

JEE Main 2026 Solution View → 6

If ∫( x)^ (-11)/(2) ( x)^ (-5)/(2) d x= - p_ 1 q_ 1 ( x)^ (9)/(2) - p_ 2 q_ 2 ( x)^ (5)/(2) - p_ 3 q_ 3 ( x)^ (1)/(2) + p_ 4 q_ 4 ( x)^ (-3)/(2) +C , where p_ i and q_ i are

JEE Main 2026 Solution View → 7

If aligned ∫((1)/(x)+(1)/(x^3)) & ( [23] 3 x^ -24 +x^ -26 ) d x & =-(α)/(3(α+1))(3 x^β+x^γ)^ (α+1)/(α) +C, x 0, aligned (α, β, γ ∈ Z) , where C is the constant of integration

JEE Main 2025 Solution View → 8

If ∫ ( 1+x^2 +x)^ 10 ( 1+x^2 -x)^9 d x= (1)/(m)(( 1+x^2 +x)^n(n 1+x^2 -x))+C where C is the constant of integration and m, n ∈ N , then m+n is equal to

JEE Main 2025 Solution View → 9

Let f(x)=∫ x^3 3-x^2 d x . If 5 f( 2 )=-4 , then f(1) is equal to

JEE Main 2025 Solution View → 10

If f(x)=∫ 1 x^ 1 / 4 (1+x^ 1 / 4 ) d x, f(0)=-6 , then f(1) is equal to :

JEE Main 2025 Solution View → 11

If ∫ 2 x^2+5 x+9 x^2+x+1 ~d x=x x^2+x+1 +α x^2+x+1 +β _e|x+(1)/(2)+ x^2+x+1 |+C , where C is the constant of integration, then α+2 β is equal to _______.

JEE Main 2025 Solution View → 12

Let ∫ x^3 x ~d x=g(x)+C , where C is the constant of integration. If 8(g((π)/(2))+g^ ((π)/(2)))=α π^3+β π^2+γ, α, β, γ ∈ Z , then α+β-γ equals :

JEE Main 2025 Solution View → 13

Let I(x)=∫ d x (x-11)^ (11)/(13) (x+15)^ (15)/(13) . If I(37)-I(24)=(1)/(4)( 1 ~b^ (1)/(13) - 1 c^ (1)/(13) ), b, c ∈ N , then 3(~b+c) is equal to

JEE Main 2025 Solution View → 14

If ∫ e^x( x ^ -1 x 1-x^2 + ^ -1 x (1-x^2)^ 3 / 2 +(x)/(1-x^2)) d x=g(x)+C , where C is the constant of integration, then g((1)/(2)) equals :

JEE Main 2025 Solution View → 15

Let ∫ (2- x)/(3+ x) ~d x=(1)/(2)(α x+ _ e |β x+γ x|)+C , where C is the constant of integration. Then α+(γ)/(β) is equal to :

JEE Main 2024 Solution View → 16

If ∫ 1 [5] (x-1)^4(x+3)^6 ~d x=A((α x-1)/(β x+3))^B+C , where C is the constant of integration, then the value of α+β+20 AB is__________

JEE Main 2024 Solution View → 17

Let I(x)=∫ (6)/( ^2 x(1- x)^2) d x . If I(0)=3 , then I((π)/(12)) is equal to

JEE Main 2024 Solution View → 18

If ∫ 1 a^2 ^2 x+b^2 ^2 x ~d x=(1)/(12) ^ -1 (3 x)+ constant, then the maximum value of a x+b x , is :

JEE Main 2024 Solution View → 19

If ∫ cosec^5 x d x=α x cosec x(cossc^2 x+(3)/(2))+β _ε| (x)/(2)|+C where α, β ∈ ℝ and C is the constant of integration, then the value of 8(α+β) equals _______

JEE Main 2024 Solution View → 20

If ∫ sin(3)/(2)x + cos(3)/(2)x ^ 3 x ^ 3 xsin ( x - θ ) dx = A cos - sinθ + B cosθ - sin + C, where C is the integration constant, then AB is equal to

JEE Main 2024 Solution View → 21

The integral ∫ ( x ^ 8 - x ^ 2 )dx ( x ^ 12 + 3 x ^ 6 + 1) ^ - 1 ( x ^ 3 + 1 x ^ 3 ) is equal to :

JEE Main 2024 Solution View → 22

Let f(x) = ∫ dx (3 + 4 x ^ 2 ) 4 - 3 x ^ 2 , |x| 0 , then α ^ 2 + β ^ 2 is equal to _______.

JEE Main 2023 Solution View → 23

∫ _ 0 ^ ∞ 6 e ^ 3x + 6 e ^ 2x + 11 e ^ x + 6 dx =

JEE Main 2023 Solution View → 24

Let I(x) = ∫ (x + 7)/(x) dx and I(9) = 12 + 7 _ e 7 . If I(1) = α + 7 _ e (1 + 2 2 ), then α ^ 4 is equal to _____.

JEE Main 2023 Solution View → 25

For α, β, γ, δ ∈ ℕ , if ∫ ( ((x)/(e)) ^ 2x + ((e)/(x)) ^ 2x ) _ e xdx = (1)/(α) ((x)/(e)) ^ - (1)/(γ) ((e)/(x)) ^ + C , where e = ∑ _ n = 0 ^ ∞ (1)/(n !) and C is constant of

JEE Main 2023 Solution View → 26

If I(x) = ∫ e ^ ^ 2 x (cosxsin2x - sinx)dx and I(0) = 1 , then I((π)/(3)) is equal to

JEE Main 2023 Solution View → 27

The integral ∫ ( ((x)/(2)) ^ x + ((2)/(x)) ^ x ) _ 2 xdx is equal to

JEE Main 2023 Solution View → 28

Let I(x) = ∫ x + 1 x (1 + x e ^ x ) ^ 2 dx, x > 0 . If _ x → ∞ I(x) = 0 then I(1) is equal to

JEE Main 2023 Solution View → 29

Let I(x) = ∫ x ^ 2 (x sec ^ 2 + tanx) ( xtanx + 1 ) ^ 2 dx If I(0) = 0, then I((π)/(4)) is equal to

JEE Main 2023 Solution View → 30

If ∫ sec2x - 1 dx = α _ e |cos2x + β + cos2x(1 + cos(1)/(β)x) | + constant, then β - α is equal to ______.

JEE Main 2023 Solution View → 31

Let f(x) = ∫ 2x ( x ^ 2 + 1)( x ^ 2 + 3) dx . If f(3) = (1)/(2)( _ e 5 - _ e 6) , then f(4) is equal to

JEE Main 2023 Solution View → 32

For I(x) = ∫ sec ^ 2 x - 2022 ^ 2022 x dx , if I((π)/(4)) = 2 ^ 1011 , then

JEE Main 2022 Solution View → 33

The integral ∫ (1 - 1 3 )(cosx - sinx) (1 + 2 3 sin2x) dx is equal to

JEE Main 2022 Solution View → 34

∫ ( x ^ 2 + 1) e ^ x (x + 1) ^ 2 dx = f(x) e ^ x + C , where C is a constant, then d ^ 3 f d x ^ 3 at x = 1 is equal to

JEE Main 2022 Solution View → 35

If ∫ (1)/(x) (1 - x)/(1 + x) dx = g(x) + c, g(1) = 0 , then g((1)/(2)) is equal to

JEE Main 2022 Solution View → 36

Let g: (0, ∞) → R be a differentiable function such that ∫ ( x(cosx - sinx) e ^ x + 1 + g(x)( e ^ x + 1 - x e ^ x ) ( e ^ x + 1) ^ 2 )dx = xg(x) e ^ x + 1 + C , for all x > 0

JEE Main 2022 Solution View → 37

If ∫ sinx ^ 3 x + ^ 3 x dx = α _ e | 1 + tanx | + β _ e |1 - tanx + ^ 2 x| + γ ^ - 1 ( 2tanx - 1 3 ) + C, when C is constant of integration, then the value of 18(α + β + γ ^ 2 ) is

JEE Main 2021 Solution View → 38

The integral ∫ 1 ( x - 1 ) ^ 3 ( x + 2 ) ^ 5 4 dx is equal to : (where C is a constant of integration)

JEE Main 2021 Solution View → 39

∫ 2 e ^ x + 3 e ^ - x 4 e ^ x + 7 e ^ - x dx = (1)/(14)(ux + v _ e (4 e ^ x + 7 e ^ - x )) + C , where C is a constant of integration, then u + v is equal to

JEE Main 2021 Solution View → 40

If ∫ dx ( x ^ 2 + x + 1) ^ 2 = a ^ - 1 ( 2x + 1 3 ) + b( 2x + 1 x ^ 2 + x + 1 ) + C, x > 0 where C is the constant of integration, then the value of 9 ( 3 a + b ) is equal to

JEE Main 2021 Solution View → 41

The integral ∫ ( 2x - 1 ) cos ( 2x - 1 ) ^ 2 + 5 4 x ^ 2 - 4x + 6 dx is equal to (where c is a constant of integration)

JEE Main 2021 Solution View → 42

If f(x) = ∫ 5 x ^ 8 + 7 x ^ 6 ( x ^ 2 + 1 + 2 x ^ 7 ) ^ 2 dx, (x ≥ 0), f(0) = 0 and f(1) = (1)/(K), then the value of K is

JEE Main 2021 Solution View → 43

For real numbers α, β, γ and δ, if ∫ ( x ^ 2 - 1) + ^ - 1 ( x ^ 2 + 1 x ) ( x ^ 4 + 3 x ^ 2 + 1) ^ - 1 ( x ^ 2 + 1 x ) dx = α _ e ( ^ - 1 ( x ^ 2 + 1 x )) + β ^ - 1 ( γ( x ^ 2

JEE Main 2021 Solution View → 44

The integral ∫ e ^ 3 _ e 2x + 5 e ^ 2 _ e 2x e ^ 4 _ e x + 5 e ^ 3 _ e x - 7 e ^ 2 _ e x dx, x > 0 , is equal to (where c is a constant of integration)

JEE Main 2021 Solution View → 45

The value of the integral ∫ sinθ · sin2θ( ^ 6 θ + ^ 4 θ + ^ 2 θ) 2 ^ 4 θ + 3 ^ 2 θ + 6 1 - cos2θ dθ is (where c is a constant of integration)

JEE Main 2021 Solution View → 46

If ∫ cosx - sinx 8 - sin2x dx = a ^ - 1 ((sinx + cosx)/(b)) + c, where c is a constant of integration, then the ordered pair (a, b) is equal to:

JEE Main 2021 Solution View → 47

If I _ 1 = ∫ _ 0 ^ 1 (1 - x ^ 50 ) ^ 100 dx and I _ 2 = ∫ _ 0 ^ 1 (1 - x ^ 50 ) ^ 101 dx such that I _ 2 = α I _ 1 then α equals to :

JEE Main 2020 Solution View → 48

If ∫ cosθ 5 + 7sinθ - 2 ^ 2 θ dθ = Alog _ e | B ( θ ) | + C, where C is a constant of integration, then (B ( θ ))/(A) can be:

JEE Main 2020 Solution View → 49

If ∫ ( e ^ 2x + 2 e ^ x - e ^ - x - 1) e ^ ( e ^ x + e ^ - x ) dx = g ( x ) e ^ ( e ^ x + e ^ - x ) + c, where c is a constant of integration, then g ( 0 ) is

JEE Main 2020 Solution View → 50

The integral ∫ ((x)/(xsinx + cosx)) ^ 2 dx is equal to, (where C is a constant of integration):

JEE Main 2020 Solution View → 51

Let f(x) = ∫ x (1 + x) ^ 2 dx(x ≥ 0) . Then f(3) - f(1) is equal to :

JEE Main 2020 Solution View → 52

If ∫ ^ - 1 ( x 1 + x )dx = A(x) ^ - 1 ( x ) + B(x) + C , where C is a constant of integration, then the ordered pair (A(x), B(x)) can be :

JEE Main 2020 Solution View → 53

If ∫ dθ ^ 2 θ(tan2θ + sec2θ) = θ + 2 _ e |f(θ)| + C where C is a constant of integration, then the ordered pair (λ, f(θ)) is equal to:

JEE Main 2020 Solution View → 54

The integral ∫ dx ( x + 4 ) ^ (8)/(7) ( x - 3 ) ^ (6)/(7) is equal to: (where C is a constant of integration)

JEE Main 2020 Solution View → 55

If ∫ cosxdx ^ 3 x(1 + ^ 6 x)(2)/(3) = f(x)(1 + ^ 6 x)(1)/(λ) + c , where c is a constant of integration, then ((π)/(3)) is equal to

JEE Main 2020 Solution View → 56

∫ (ln ⁡ (x + 1) - ln ⁡ x)/(x(x + 1))dx is equal to (where C is an arbitarary constant)

NTA Abhyas JEE Main 2020 Solution View → 57

The integral ∫ x cos ^ - 1 ( 1 - x ^ 2 1 + x ^ 2 ) dx; (x > 0) is equal to

NTA Abhyas JEE Main 2020 Solution View → 58

∫ ^ 4 ⁡ x ^ 8 ⁡ x dx is equal to (where C is an arbitrary constant)

NTA Abhyas JEE Main 2020 Solution View → 59

If m is any natural number, then the value of the integral ∫ (x^ 3m + x^ 2m + x^ m ) (2x^ 2m + 3x^ m + 6) ^ (1 / m) dx is (where, C & is an arbitrary constant)

NTA Abhyas JEE Main 2020 Solution View → 60

∫ ^ 8 x - ^ 8 x 1 - 2 ^ 2 x ^ 2 x dx is equal to (where C is an arbitrary constant)

NTA Abhyas JEE Main 2020 Solution View → 61

If ∫ dx x + x 3 = a x + b(x 3) + c(x 6) + dln ( x6 + 1 ) + e, e being an arbitrary constant, then the value of 20a + b + c + d is

NTA Abhyas JEE Main 2020 Solution View → 62

If I = ∫ ( tan ⁡ x + cot ⁡ x )dx , then I equals to (where, C & is an arbitrary constant)

NTA Abhyas JEE Main 2020 Solution View → 63

The graph of the antiderivative of f(x) = x e ^ (x)/(2) passes through (0, 3) , then the value of g(2) - f(0) is

NTA Abhyas JEE Main 2020 Solution View → 64

If the integral ∫ 5 x x - 2 dx = x + a | x - 2 x| + k , then the value of a is

NTA Abhyas JEE Main 2020 Solution View → 65

Let f(x) = (9x)/(25) + c, c > 0 . If the curve y = f ^ - 1 (x) passes through ((1)/(4), - (5)/(4)) and g (x) is the antiderivative of f ^ - 1 (x) such that g(0) = (5)/(2), then

NTA Abhyas JEE Main 2020 Solution View → 66

∫ ( x - 1 x + 1 ) x^ 2 - 1 dx is equal to

NTA Abhyas JEE Main 2020 Solution View → 67

The value of ∫ dx x( x^ n + 1 ) is equal to

NTA Abhyas JEE Main 2020 Solution View → 68

The value of ∫ (sin ⁡ 101x) . ^ 99 ⁡ xdx is sin ⁡ (100x) ^ 100 ⁡ x k + 5 , then (k)/(19) is

NTA Abhyas JEE Main 2020 Solution View → 69

If ∫ dx (x - 1) ^ 3 / 4 (x + 2) ^ 5 / 4 = k ( x - 1 x + 2 ) ^ 1 / 4 + c , then the number of divisors of 30k is

NTA Abhyas JEE Main 2020 Solution View → 70

If ∫ x ^ pq - p - 1 ( x ^ p + 1) ^ q dx = 2 ( 1+ x ^ - p ) ^ 1 - q ( q - 1 ) + c(p, q ∈ N - 1 ) , then the value of λ is (here, c is an arbitrary constant)

NTA Abhyas JEE Main 2020 Solution View → 71

The value of the integral ∫ e^ 3sin^ - 1 x ( 1 1 - x^ 2 + e^ 3cos^ - 1 x )dx is equal to (where, c & is an arbitrary constant)

NTA Abhyas JEE Main 2020 Solution View → 72

The value of the integral ∫ ((sin ⁡ x)/(x))^ 6 ((xcosx - sin ⁡ x)/(x2))dx is (where, c & is an arbitrary constant)

NTA Abhyas JEE Main 2020 Solution View → 73

If the integral Ι = ∫ x^ sinx (cosx ⋅ ln ⁡ x + (sinx)/(x))dx = (f (x))g (x) + c(∀ x > 0) , then the range of y = g (x) is (where, c & is an arbitrary constant)

NTA Abhyas JEE Main 2020 Solution View → 74

If the value of integral ∫ dx (x + x^ 2 - 1 ) ^ 2 = ax^ 3 - x + b (x^ 2 - 1) ^ (1)/(b) + C , (where, C is the constant of integration), then a × b & is equal to

NTA Abhyas JEE Main 2020 Solution View → 75

The value of the integral ∫ x^ 2 - 4x x + 6x - 4 x + 1 x - 2 x + 1 dx & is equal to

NTA Abhyas JEE Main 2020 Solution View → 76

If f(x) = sin ⁡ x, g(x) = cos ⁡ x and h(x) = cos(cos ⁡ x), then the integral Ι = ∫ f(g(x)) . f(x) . h(x)dx simplifies to - λ ^ 2 ⁡ (cos ⁡ x) + C (where, C is the constant of

NTA Abhyas JEE Main 2020 Solution View → 77

The value of the integral ∫ sin^ 2 xsec^ 2 x + 2 1 - x^ 2 tanxsin^ - 1 x 1 - x^ 2 (1 + tan^ 2 x) dx is (where, C is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 78

If a function f: R → R is defined as f(x) = ∫ x^ 8 + 4 x^ 4 - 2x^ 2 + 2 dx and f(0) = 1 , then which of the following is correct?

NTA Abhyas JEE Main 2020 Solution View → 79

The value of ∫ (x - 4) x^ 2 x - 2 dx is equal to (where, C is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 80

The value of ∫ xdx ( x + 3 ) x + 1 is (where, c & is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 81

If ∫ e^ sin ⁡ θ (sin ⁡ θ + ^ 2 ⁡ θ)dθ is equal to f(θ) + C (where, C is the constant of integration) and f (0) = 0 , then the value of f ((π)/(4)) is

NTA Abhyas JEE Main 2020 Solution View → 82

If f ( x ) is the antiderivative of (1 + 2tanx ( tanx + secx ))(1)/(2) and f((π)/(6)) = log2 , then the value of f ( 0 ) is

NTA Abhyas JEE Main 2020 Solution View → 83

The integral Ι = ∫ (sin( x ^ 2 ) + 2 x ^ 2 cos( x ^ 2 ))dx = xH(x) + C, (where C is the constant of integration). If the range of H ( x ) is [a, b] , then the value of a + 2b is

NTA Abhyas JEE Main 2020 Solution View → 84

Let ∫ e ^ x ⋅ x ^ 2 dx = f(x) e ^ x + C (where, C is the constant of integration). The range of f(x) as x ∈ R is [a, ∞) . The value of (a)/(4) is

NTA Abhyas JEE Main 2020 Solution View → 85

The value of ∫ e^ x x (1 + e^ 2 x ) dx is equal to (where, C is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 86

The integral I = ∫ 2 ^ ( 2 ^ x + x) dx = λ. ( 2 ^ 2 ^ x ) + C (where, C is the constant of integration). Then the value of& λ and is equal to

NTA Abhyas JEE Main 2020 Solution View → 87

The value of ∫ cos ⁡ x ^ 2 ⁡ x(sin ⁡ x + cos ⁡ x) dx is equal to

NTA Abhyas JEE Main 2020 Solution View → 88

If the integral ∫ x^ 4 + x^ 2 + 1 x^ 2 - x + 1 dx = f(x) + C, (where C is the constant of integration and x ∈ ℝ ), then the minimum value of f^ ' (x) is&

NTA Abhyas JEE Main 2020 Solution View → 89

If I _ n = ∫ (ln ⁡ x)ndx , then I _ 10 + 10 I _ 9 is equal to (where C & is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 90

The value of the integral ∫ x^ (1)/(3) (1 - x ) ^ 3 dx is equal to (where c & is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 91

The value of the integral Ι = ∫ e^ x (sin ⁡ x + cos ⁡ x)dx is equal to e^ x ⋅ f(x) + C,C being the constant of integration. Then the maximum value of y = f(x^ 2 ), ∀ x ∈ ℝ is

NTA Abhyas JEE Main 2020 Solution View → 92

If Ι = ∫ tan^ - 1 (e^ x ) e^ x + e^ - x dx = [tan^ - 1 (f(x))]2 2 + C (where C is the constant of integration), then the range of y = f(x) ∀ x ∈ ℝ is

NTA Abhyas JEE Main 2020 Solution View → 93

The value of the integral ∫ cosec^ 2 x - 2019 cos^ 2019 x dx is equal to (where C & is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 94

Let A _ n = ∫ ^ n ⁡ xdx, ∀ n ∈ ℕ . If A _ 10 + A _ 12 = ^ m ⁡ x m + λ (where λ is an arbitrary constant), then the value of m & is equal to

NTA Abhyas JEE Main 2020 Solution View → 95

The value of the integral ∫ e^ x^ 2 + (1)/(x) (2x^ 2 - (1)/(x) + 1)dx is equal to (where C is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 96

If ∫ dx e^ x - 1 = 2tan^ - 1 (f(x)) + C, (where x > 0 and C is the constant of integration) then the range of f (x) is

NTA Abhyas JEE Main 2020 Solution View → 97

Let f(n, x) = ∫ ncos(nx)dx, with f (n, 0) = 0. If the expression ∑ _ x = 1 ^ 89 f(1, x) simplifies to (sin ⁡ asin ⁡ b)/(sin ⁡ c), then the value of (b)/(ac) is (where a > b )

NTA Abhyas JEE Main 2020 Solution View → 98

If ∫ co s ^ 4 xdx si n ^ 3 x (si n ^ 5 x + co s ^ 5 x) ^ (3)/(5) = - (1)/(K) (1 + co t ^ P x) ^ (K)/(P) + C , then the value of K + P is equal to (where C is the constant of

NTA Abhyas JEE Main 2020 Solution View → 99

If ∫ dx x^ 2 + x = ln ⁡ |f(x)| + C (where C is the constant of integration), then the range of y = f(x), ∀ x ∈ ℝ - \ - 1,0\ is

NTA Abhyas JEE Main 2020 Solution View → 100

If Ι = ∫ dx x^ 3 (x^ 8 + 1)^ 3 / 4 = λ(1 + x^ 8 )(1)/(4) x2 + c (where c is the constant of integration), then the value of λ & is equal to

NTA Abhyas JEE Main 2020 Solution View → 101

The value of ∫ (tan^ - 1 (sin ⁡ x + 1))cos ⁡ x (3 + 2sin ⁡ x - cos^ 2 x) dx is (where c & is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 102

Let Ι = ∫ cos^ 3 x 1 + sin^ 2 x dx, then Ι is equal to (where c is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 103

The value of ∫ 1 (2x - 1) x^ 2 - x dx is equal to (where c & is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 104

The value of ∫ (1 - cos ⁡ θ) ^ (3)/(10) (1 + cos ⁡ θ) ^ (13)/(10) dθ is equal to (where, c & is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 105

The integral Ι = ∫ e^ x ((1 + sin ⁡ x)/(1 + cos ⁡ x))dx = e^ x f (x) + C (where, C is the constant of integration). Then, the range of y = f(x) (for all x in the domain of f (x) )

NTA Abhyas JEE Main 2020 Solution View → 106

Let ∫ dx x^ 2 + 1 - x = f(x) + C such that f (0) = 0 and C is the constant of integration, then the value of f(1) is

NTA Abhyas JEE Main 2020 Solution View → 107

If the integral Ι = ∫ e^ sin ⁡ x (cos ⁡ x ⋅ x^ 2 + 2x)dx =e^ f(x) g(x) + C (where, C is the constant of integration), then the number of solution(s) of f (x) = g (x) is/are

NTA Abhyas JEE Main 2020 Solution View → 108

The value of ∫ sin^ 3 x cos ⁡ x dx is equal to (where, c & is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 109

The value of the integral Ι = ∫ (dx)/(1 + sinx), ∀ x ∈ [0, (π)/(2)] is equal to& kln ⁡ (tan((π)/(4) + (x)/(8))) + c, then the value of k 2 is equal to (where, c is the constant of

NTA Abhyas JEE Main 2020 Solution View → 110

The value of ∫ (ln ⁡ ( x))/(sin ⁡ 2x)dx is equal to (where, C is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 111

If the integral ∫ (ln ⁡ x)/(x3)dx = f(x) 4x^ 2 + C , where f (e) = - 3 and& C is the constant of integration,& then the value of& f(e^ 2 ) & is equal to

NTA Abhyas JEE Main 2020 Solution View → 112

If the integral Ι = ∫ e ^ x ^ 2 x ^ 3 dx = 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

NTA Abhyas JEE Main 2020 Solution View → 113

The value of the ∫ ( sin^ 8 x - cos^ 8 x 1 - 2sin^ 2 xcos^ 2 x )dx is equal to (where, C is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 114

The value of the integral Ι = ∫ 2x^ 9 + x^ 10 (x^ 2 + x^ 3 ) ^ 3 dx is equal to (where, C is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 115

The value of the integral ∫ dx (1 + x ) x - x^ 2 is equal to (where, C & is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 116

If the integral Ι = ∫ dx x^ 10 + x = ( x^ 9 1 + x^ μ ) + C, (where, C is the constant of integration) then the value of (1)/(λ) + μ & is equal to

NTA Abhyas JEE Main 2020 Solution View → 117

Let the integral I = ∫ (2020)x + ^ -1 ⁡ (2020)x 1 - (2020)2x dx= K^ 2 (2020) ^ -1 ⁡ (2020)x + λ (where, λ is the constant of integration), then the vaue of 2020 ^ K & is

NTA Abhyas JEE Main 2020 Solution View → 118

Let ∫ sin ⁡ (2x)ln ⁡ ( cos ⁡ x ) dx = ⁡f ( x ) ^ 2 ⁡ x +C, (where, C is the constant of integration) and f(0) = (1)/(2) . If f((π)/(3)) is equal to (1)/(a) + ln ⁡ b, then the

NTA Abhyas JEE Main 2020 Solution View → 119

If the integral I = ∫ e ^ 5ln ⁡ x ( x ^ 6 + 1) ^ - 1 dx = ln ⁡ ( x ^ 6 + 1) + C , (where, C is the constant of integration) then the value of (1)/(λ) is

NTA Abhyas JEE Main 2020 Solution View → 120

If f (x) is a differentiable function such that ∫ f(x)dx = 2 left[f(x)] ^ 2 + C , (where, C is the constant of integration) and f (1) = 1 / 4, then f(π) equals

NTA Abhyas JEE Main 2020 Solution View → 121

If I = ∫ 1 + x ^ 4 (1 - x ^ 4 )(3)/(2) dx = 1 f(x) + C (where, C is the constant of integration) and f(2) = (- 15)/(4) , then the value of 2f( 1 2 ) is

NTA Abhyas JEE Main 2020 Solution View → 122

Let I = ∫ dx 1 + 3si n ^ 2 x = (1)/(2) tan ^ - 1 (2f(x)) + C (where, C is the constant of integration). If f((π)/(4)) = 1, then the fundamental period of y = f(x) is

NTA Abhyas JEE Main 2020 Solution View → 123

If 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

NTA Abhyas JEE Main 2020 Solution View → 124

If the integral I = ∫ x^ 5 1 + x^ 3 dx = K x^ 3 + 1 (x^ 3 - 2) + C, (where, C is the constant of integration), then the value of 9K & is equal to

NTA Abhyas JEE Main 2020 Solution View → 125

Let I = ∫ dx (cos ⁡ x - sin ⁡ x) ^ 2 = (1)/(f(x)) + C (where, C is the constant of integration). If f((π)/(3)) = 1 - 3 , then the number of solution(s) of f(x) = 2020 in x ∈

NTA Abhyas JEE Main 2020 Solution View → 126

If the integral I = ∫ (- (sin ⁡ x)/(x) - ln ⁡ xcos ⁡ x)dx= f(x) + C (where, C is the constant of integration) and f(e) = - sin ⁡ e, then the number of natural numbers less than

NTA Abhyas JEE Main 2020 Solution View → 127

The integral I = ∫ ^ 3 ⁡ x ^ 3 ⁡ xdx is equal to (where, C is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 128

The integral I = ∫ e ^ x cos ⁡ ( e ^ x ) x dx = f(x) + c (where, c is the constant of integration) and f (ln ⁡ ((π)/(4))) ^ 2 = 2 . Then, the number of solutions of f(x) = 2e(∀ x

NTA Abhyas JEE Main 2020 Solution View → 129

Consider the integrals I = ∫ (sin ⁡ x)/(3cos ⁡ x + 4sin ⁡ x)dx and J = ∫ (cos ⁡ x)/(3cos ⁡ x + 4sin ⁡ x)dx. Then, the integral 4J - 3I is equal to (where, c is the constant of

NTA Abhyas JEE Main 2020 Solution View → 130

If I = ∫ x^ 5 + 1 x + 1 dx= f(x) + c and f(0) = 0 (where, c is the constant of integration), then

NTA Abhyas JEE Main 2020 Solution View → 131

If the integral I = ∫ x x - 3x + 3 x - 1 x - 2 x + 1 dx= f(x) + C (where, x > 0 and& C is the constant of integration) and f (1) = (- 1)/(3), then the value of& f(9) & is equal to

NTA Abhyas JEE Main 2020 Solution View → 132

If the integral I = ∫ 2x^ 2 4 + x^ 2 dx = 2x - f(x) + c , where f (2) = π, then the minimum value of y = f(x) ∀ x ∈ [-2,2] is (where, c is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 133

Consider the integrals I _ 1 = ∫ e^ x2 cos ⁡ xdx and I _ 2 = ∫ xe^ x2 sin ⁡ xdx. Then, I _ 1 + 2 I _ 2 simplifies to (where, c is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 134

If B = ∫ 1 e^ x + 1 dx= - f ( x ) + C , where, C is the constant of integration and e^ f(0) = 2, then the value of e^ f(- 1) is

NTA Abhyas JEE Main 2020 Solution View → 135

The integral I = ∫ [xe^ x2 (sin ⁡ x^ 2 + cos ⁡ x^ 2 )]dx= f (x) + c, (where, c is the constant of integration). Then, f(x) can be

NTA Abhyas JEE Main 2020 Solution View → 136

If I = ∫ dx x^ 2 - 2x + 5 = (1)/(2)tan ⁡ ^ - 1 (f(x)) + C (where, C is the constant of integration) and f(2) = (1)/(2) , then the maximum value of y = f(sin ⁡ x) ∀ x ∈ ℝ is

NTA Abhyas JEE Main 2020 Solution View → 137

The least value of n (n ∈ ℕ) , such that the function f(n, x) = ∫ ncos ⁡ (nx)dx satisfies f(n, (π)/(2)) = -1 , is (given, f(n, 0) =0 )

NTA Abhyas JEE Main 2020 Solution View → 138

The integral I = ∫ (e(e^ sin ⁡ x + sin ⁡ x))cos ⁡ xdx simplifies to (where, c is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 139

If I _ n = ∫ x^ n e^ 6x dx , then the expression 6 I _ 10 + 10 I _ 9 simplifies to (where, c is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 140

The integral I = ∫ ((1)/(x ⋅ sec ⁡ x) - ln ⁡ (x^ sin ⁡ x ))dx simplifies to (where, c is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 141

The indefinite integral I = ∫ sec ^ 2 ⁡ xtan ⁡ x(sec ⁡ x + tan ⁡ x)dx ( sec ^ 5 ⁡ x + sec ^ 2 ⁡ x ^ 3 ⁡ x - sec ^ 3 ⁡ x ^ 2 ⁡ x - ^ 5 ⁡ x) simplifies to (1)/(3)ln ⁡ |f(x)| + c

NTA Abhyas JEE Main 2020 Solution View → 142

The indefinite integral ∫ e ^ e ^ x ( x e ^ x ⋅ ln ⁡ x + 1 x )dx simplifies to (where, c is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 143

If I = ∫ x ^ 3 - 1 x ^ 5 + x ^ 4 + x + 1 dx = (1)/(4)ln ⁡ (f(x)) - ln ⁡ (g(x)) + c (where, c is the constant of integration) and f(0) = g(0) = 1 , then the value of f(1) ⋅ g(1) is

NTA Abhyas JEE Main 2020 Solution View → 144

If& I = ∫ dx x^ (5)/(2) (1 + x) ^ (7)/(2) 3 = kf(x) + c, where& c is the integration constant and f (1) = (1)/(2(1)/(6)), then the value of& f(2) & is equal to

NTA Abhyas JEE Main 2020 Solution View → 145

The integral I = ∫ ^ 3 ⁡ ⁡ θ (1 + ^ 2 ⁡ θ) ^ 2 dθ simplifies to (where, c is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 146

The integral I = ∫ 2sin ⁡ x(3 + sin ⁡ 2x)dx simplifies to (where, C is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 147

If the integral I = ∫ tan ⁡ x 5 + 7 ^ 2 ⁡ x dx = kln ⁡ |f(x)| + C (where C is the integration constant) and f(0) = 5 , then the value of f((π)/(4)) is equal to

NTA Abhyas JEE Main 2020 Solution View → 148

The integral I = ∫ sin ⁡ (2θ)[ 1 + ^ 2 ⁡ θ 2 ^ 2 ⁡ θ ]dθ simplifies to (where, c is the integration constant)

NTA Abhyas JEE Main 2020 Solution View → 149

If ∫ f(x)dx = 3[f(x)]2 + c (where c is the constant of integration) and f (1) = (1)/(6),then f (6π)& is equal to

NTA Abhyas JEE Main 2020 Solution View → 150

If I = ∫ (ln ⁡ x)^ 5 x^ 2 + x^ 2 (ln ⁡ x)^ 3 dx =k (ln ⁡ x)^ 3 + 1 ((ln ⁡ x)^ 3 - 2) + c (where c is the constant of integration), then 9k & is equal to

NTA Abhyas JEE Main 2020 Solution View → 151

The indefinite integral I = ∫ ( ^ 2 ⁡ x - ^ 2 ⁡ x) ^ 2019 (sin ⁡ x) ^ 2021 (cos ⁡ x) ^ 2021 dx simplifies to (where c is an integration constant)

NTA Abhyas JEE Main 2020 Solution View → 152

Let f(x) = 2x + 1 and g(x) = ∫ f(x) x^ 2 (x + 1) ^ 2 dx . If 6g (2) + 1 = 0, then g(- (1)/(2)) is equal to

NTA Abhyas JEE Main 2020 Solution View → 153

If ∫ 2x^ 2 + 5 x^ 2 + a dx = f (x) , where f (x) is a polynomial or ratio of polynomials, then the number of possible value(s) of a is equal to

NTA Abhyas JEE Main 2020 Solution View → 154

Consider ∫ 3 x ^ 4 + 2 x ^ 2 + 1 x ^ 4 + x ^ 2 + 1 dx = f(x) . If f(1) = 3 , then (f(2)) ^ 2 is equal to

NTA Abhyas JEE Main 2020 Solution View → 155

If I = ∫ (sin ⁡ x)/(3sin ⁡ x + cos ⁡ x + 2)dx and J = ∫ (cos ⁡ x)/(3sin ⁡ x + cos ⁡ x + 2)dx , then 3J - I is equal to (where C is the constant of integration)

NTA Abhyas JEE Main 2020 Solution View → 156

Let ∫ 1 - ln ⁡ x x^ 2 dx = f(x), for all positive x . If f (e) = (1)/(e), then f(2) + f (4) is equal to

NTA Abhyas JEE Main 2020 Solution View → 157

If ∫ dx (x + 1) ^ 2 ( x ^ 2 + 2x + 2) = (A)/(x + 1) + B ^ - 1 ⁡ (x + 1) + C, where A and B are constants and C is the constant of integration, then |A - B| is equal to

NTA Abhyas JEE Main 2020 Solution View → 158

If ∫ x x + 1 + e^ x dx = px + qln ⁡ |x + 1 + e^ x | + c, where c is the constant of integration, then p + q is equal to

NTA Abhyas JEE Main 2020 Solution View → 159

Let ∫ x ^ 3 + x ^ 2 + x 12 x ^ 3 + 15 x ^ 2 + 20x dx = f(x) where f(1) = 47 30 . If (f(2)) ^ 2 is equal to (p)/(225), then the value of p is equal to

NTA Abhyas JEE Main 2020 Solution View → 160

Let α ∈ ( 0, (π)/(2) ) , be constant.If the integral ∫ (tanx + tanα)/(tanx - tanα)dx = A(x)cos2α + B(x)sin2α + C , where C is a constant of integration, then the functions A ( x )

JEE Main 2019 Solution View → 161

The integral ∫ 2 x ^ 3 - 1 x ^ 4 + x dx , is equal to

JEE Main 2019 Solution View → 162

If ∫ x ^ 5 e ^ - x ^ 2 dx = g(x) e ^ - x ^ 2 + c , where c is a constant of integration, then g(- 1) is equal to

JEE Main 2019 Solution View → 163

If ∫ dx ( x ^ 2 - 2x + 10) ^ 2 = A( ^ - 1 ((x - 1)/(3)) + f(x) x ^ 2 - 2x + 10 ) + C , then (where C is a constant of integration)

JEE Main 2019 Solution View → 164

If ∫ e ^ secx (secxtanxf(x) + (secxtanx + se c ^ 2 x))dx = e ^ secx f(x) + C, then a possible choice of f(x) is:

JEE Main 2019 Solution View → 165

∫ se c ^ 2 x · cot(4)/(3)xdx is equal to

JEE Main 2019 Solution View → 166

If ∫ dx x ^ 3 (1 + x ^ 6 )(2)/(3) = xf(x)(1 + x ^ 6 )(1)/(3) + C , where C is a constant of integration, then the function f(x) is equal to

JEE Main 2019 Solution View → 167

∫ (sin(5x)/(2))/(sin(x)/(2))dx , is equal to

JEE Main 2019 Solution View → 168

The integral ∫ 3 x ^ 13 + 2 x ^ 11 (2 x ^ 4 + 3 x ^ 2 + 1) ^ 4 dx , is equal to

JEE Main 2019 Solution View → 169

The integral ∫ cos(lnx)dx , is equal to

JEE Main 2019 Solution View → 170

If ∫ x+1 2 x-1 ~d x=f(x) 2 x-1 +C, where C is a constant of integration, then f(x) is equal to:

JEE Main 2019 Solution View → 171

If ∫ 1-x^ 2 x^ 4 d x=A(x)( 1-x^ 2 )^ m +C, for a suitable chosen integer m and a function A(x) , where C is a constant of integration, then (A(x))^ m equals :

JEE Main 2019 Solution View → 172

If ∫ x ^ 5 e ^ - 4 x ^ 3 dx = (1)/(48) e ^ - 4 x ^ 3 f(x) + C , where C is a constant of integration, then f(x) is equal to

JEE Main 2019 Solution View → 173

Let, n ≥ 2 be a natural number and 0 < θ < (π)/(2) . Then ∫ (si n ^ n θ - sinθ)(1)/(n)cosθ si n ^ n + 1 θ dθ, is equal to

JEE Main 2019 Solution View → 174

If f(x) = ∫ (5 x ^ 8 + 7 x ^ 6 ) ( x ^ 2 + 1 + 2 x ^ 7 ) ^ 2 dx , (x ≥ 0), and f(0) = 0, then the value of f ( 1 ) is

JEE Main 2019 Solution View → 175

For, x ^ 2 ≠ nπ + 1, n ∈ N (the set of natural numbers), the integral ∫ x 2sin( x ^ 2 - 1) - sin2( x ^ 2 - 1) 2sin( x ^ 2 - 1) + sin2( x ^ 2 - 1) dx , is equal to (where c is a

JEE Main 2019 Solution View → 176

If ∫ tanx 1 + tanx + ^ 2 x dx = x - K A ^ - 1 ( Ktanx + 1 A ) + C , ( C is a constant of integration), then the ordered pair (K, A) is equal to

JEE Main 2018 Solution View → 177

∫ 2 x+5 7-6 x-x^2 d x=A 7-6 x-x^2 + B ^ -1 ((x+3)/(4))+ C (where C is a constant of integration), then the ordered pair (A, B) is equal to

JEE Main 2018 Solution View → 178

If f((x-4)/(x+2))=2 x+1,(x ∈ R=\ 1,-2\ ) , then ∫ f ( x ) d x is equal to (where C is a constant of integration)

JEE Main 2018 Solution View → 179

If f((x - 4)/(x + 2)) = 2x + 1, (x ∈ R - \ 1, - 2\ ) , then ∫ f(x)dx is equal to

JEE Main 2018 Solution View → 180

The integral ∫ ^ 2 x ^ 2 x ( ^ 5 x + ^ 3 x ^ 2 x + ^ 3 x ^ 2 x + ^ 5 x) ^ 2 dx , is equal to (where C is the constant of integration).

JEE Main 2018 Solution View → 181

If f((3x - 4)/(3x + 4)) = x + 2, x ≠ - (4)/(3) , and ∫ f(x)dx = Alog|1 - x| + Bx + C , then the ordered pair (A, B) is equal to

JEE Main 2017 Solution View → 182

The integral ∫ 1 + 2cotx(cosecx + cotx) dx, (0 < x < (π)/(2)) is equal to

JEE Main 2017 Solution View → 183

Let, I _ n = ∫ ^ n xdx (n > 1) . If I _ 4 + I _ 6 = a ^ 5 x + b x ^ 5 + c, then the ordered pair (a, b), is equal to

JEE Main 2017 Solution View → 184

The integral &int; dx (1 + x ) x - x ^ 2 is equal to

JEE Main 2016 Solution View → 185

If ∫ dx ^ 3 x 2sin2x = (tanx) ^ A + C (tanx) ^ B + k , where k is a constant of integration, then A + B + C equals

JEE Main 2016 Solution View → 186

The integral ∫ 2 x ^ 12 + 5 x ^ 9 ( x ^ 5 + x ^ 3 + 1) ^ 3 dx , is equal to

JEE Main 2016 Solution View → 187

If ∫ log(t + 1 + t ^ 2 ) 1 + t ^ 2 dt = (1)/(2) (g(t)) ^ 2 + c , where c is a constant, then g(2) , is equal to

JEE Main 2015 Solution View → 188

The integral ∫ (dx)/((x + 1)(3)/(4)(x - 2)(5)/(4)) , is equal to

JEE Main 2015 Solution View → 189

The integral ∫ dx x ^ 2 ( x ^ 4 + 1)(3)/(4) equals to

JEE Main 2015 Solution View → 190

If m is a non-zero number and ∫ x ^ 5m - 1 + 2 x ^ 4m - 1 ( x ^ 2m + x ^ m + 1) ^ 3 dx = f(x) + c, then f(x) is equal to

JEE Main 2014 Solution View → 191

The integral ∫ ( ^2 x ^2 x)/(( ^3 x+ ^3 x)^2) d x is equal to:

JEE Main 2014 Solution View → 192

The integral ∫ x ^ -1 ((1-x^2)/(1+x^2)) d x(x>0) is equal to:

JEE Main 2014 Solution View → 193

∫ ^ 8 x - ^ 8 x (1 - 2 ^ 2 x ^ 2 x) dx is equal to

JEE Main 2014 Solution View → 194

The integral ∫ (1 + x - (1)/(x)) e ^ x + (1)/(x) dx , is equal to

JEE Main 2014 Solution View → 195

If the integral ∫ ( 8 x+1)/( 2 x- 2 x) d x=A 8 x+k where k is an arbitrary constant, then A is equal to:

JEE Main 2013 Solution View → 196

The integral ∫ x d x 2-x^2+ 2-x^2 equals :

JEE Main 2013 Solution View → 197

If ∫ (x^2-x+1)/(x^2+1) e^ ^ -1 x d x=A(x) e^ ^ -1 x +C , then A(x) is equal to :

JEE Main 2013 Solution View → 198

If ∫ (d x)/(x+x^7)=p(x) then, ∫ (x^6)/(x+x^7) d x is equal to:

JEE Main 2013 Solution View → 199

If ∫ f( x )dx = ψ( x ) , then ∫ x ^ 5 f( x ^ 3 )dx , is equal to

JEE Main 2013 Solution View → 200

The integral ∫ ^ 2 x ( x+ x)^ (9)/(2) d x equals (for some arbitrary constant K )

JEE Advanced 2012 Solution View →
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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

Indefinite Integration in other exams

NDA Indefinite Integration (77)BITSAT Indefinite Integration (21)