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JEE Main Indefinite Integration questions

24 Mathematics questions on Indefinite Integration as asked in JEE Main, newest first. 15 come with a worked solution.

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

    2023

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

    2019

  3. The integral ∫ sec^2/3 x cosec^4/3 x dx is equal to (here C is a constant of integration)

    2019 · with solution

  4. Let α ∈ (0, π/2) be fixed. If the integral ∫ (tan x + tan α)/(tan x - tan α) dx = A(x) cos 2α + B(x) sin 2α + C, where C is a constant of integration, then the functions A(x) and B(x) are respectively

    2019

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

    2019

  6. If ∫ e^sec x (sec x tan x f(x) + (sec x tan x + sec^2 x)) dx = e^sec x f(x) + C, then a possible choice of f(x) is

    2019 · with solution

  7. The integral ∫ cos(log_e x) dx is equal to (where C is a constant of integration)

    2019 · with solution

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

    2019 · with solution

  9. If ∫ dfracdxx^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

    2019 · with solution

  10. ∫ (sin 5x/2)/(sin x/2) dx is equal to (where, C is a constant of integration)

    2019 · with solution

  11. The integral ∫ dfrac3x^13 + 2x^11(2x^4 + 3x^2 + 1)^4 dx is equal to (where C is a constant of integration)

    2019

  12. If ∫ dfracx+1√(2x-1) dx = f(x)√(2x-1) + C, where C is a constant of integration, then f(x) is equal to

    2019 · with solution

  13. If ∫ dfrac√(1-x^2)x^4 dx = 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

    2019

  14. For x^2 ≠ nπ + 1, n ∈ N (the set of natural numbers), the integral ∫ x√((2sin(x^2-1)-sin 2(x^2-1))/(2sin(x^2-1)+sin 2(x^2-1))) dx is equal to (where C is a constant of integration)

    2019

  15. The integral ∫ (sin^2 x cos^2 x)/( (sin^5 x + cos^3 x sin^2 x + sin^3 x cos^2 x + cos^5 x )^2) dx is equal to

    2018

  16. Let I_n = ∫ tan^n x dx (n > 1). If I_4 + I_6 = a tan^5 x + bx^5 + C, where C is a constant of integration, then the ordered pair (a, b) is equal to

    2017 · with solution

  17. The integral ∫ dfrac2x^12 + 5x^9(x^5 + x^3 + 1)^3 dx is equal to

    2016 · with solution

  18. The value of ∫ dfracdxx^2(x^4+1)^3/4 is

    2015 · with solution

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

    2013 · with solution

  20. If I = ∫ frace^xe^4x + e^2x + 1 dx, J = ∫ frace^-xe^-4x + e^-2x + 1 dx. Then, for an arbitrary constant c, the value of J - I equals

    2008 · with solution

  21. If f(x) = dfracx(1+x^n)^1/n for n ≥ 2 and g(x) = underbrace(f o f o … o f)_f occurs n times(x). Then ∫ x^n-2 g(x) dx equals

    2007 · with solution

  22. The value of ∫ dfrac(x^2-1) dxx^3√(2x^4-2x^2+1) is \hfill

    2006 · with solution

  23. The value of ∫ (cos^3 x + cos^5 x)/(sin^2 x + sin^4 x) dx is

    1995

  24. ∫ (1 + x - 1/x ) e^x + 1/x dx is equal to

    with solution

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