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NDA Indefinite Integration PYQs with Solutions

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

77 questionsMathematics2010–2026Answers + solutions

About Indefinite Integration PYQs

Indefinite Integration has 77 previous year questions in the Quantrex Academy NDA Mathematics bank. The 77 questions in this list come from NDA (77), spanning 2010 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Indefinite Integration PYQs with Solutions

About Indefinite Integration PYQs

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Indefinite Integration questions with solutions

Passage: Let ∫( θ\,dθ)/((2+ θ)(3+4 θ))=A |2+ θ|+B |3+4 θ| . Question: What is the value of A ?

Passage: Let ∫( θ\,dθ)/((2+ θ)(3+4 θ))=A |2+ θ|+B |3+4 θ| . Question: What is the value of B ?

What is ∫ dx 10^x + 10^ -x equal to?

Consider the following for the two (02) items that follow: Let the function y = (1 - x)^ -1 , where x ≠ 2nπ and n is an integer. What is ∫ y \, dx equal to?

For the following two (02) items: Let u = ∫ e^x x\, dx and v = ∫ e^x x\, dx . Consider the following: I. (du)/(dx) = -v II. (dv)/(dx) = -u Which of the above is/are correct?

For the following two (02) items: Let u = ∫ e^x x\, dx and v = ∫ e^x x\, dx . What is u + v equal to?

Let ∫ d x x+1 - x-1 =α(x+1)^ (3)/(2) +β(x-1)^ (3)/(2) +c What is the value of β ?

Paragraph: Let 2 ∫ x^2-1 x^2+1 d x=U(x) V(x)-3 \ U(x)+V(x)\ +c Question: What is U(x) V(x) equal to?

Paragraph: Let 2 ∫ x^2-1 x^2+1 d x=U(x) V(x)-3 \ U(x)+V(x)\ +c Question: What is |U^2(x)-V^2(x)| equal to?

Given that ∫ (3 x+4 x)/(2 x+5 x) d x=(α x)/(29)+(β)/(29) |2 x+5 x|+c What is the value of β ?

Given that ∫ (3 x+4 x)/(2 x+5 x) d x=(α x)/(29)+(β)/(29) |2 x+5 x|+c What is the value of α ?

Let ∫ d x x+1 - x-1 =α(x+1)^ (3)/(2) +β(x-1)^ (3)/(2) +c What is the value of α ?

Paragraph: Let f(x)=P e^x+Q e^ 2 x +R e^ 3 x , where P, Q, R are real numbers. Further f(0)=6, f^ ( 3)=282 and ∫_0^ 2 f(x) d x=11 Question: What is the value of R ?

Paragraph: Let f(x)=P e^x+Q e^ 2 x +R e^ 3 x , where P, Q, R are real numbers. Further f(0)=6, f^ ( 3)=282 and ∫_0^ 2 f(x) d x=11 Question: What is the value of Q ?

What is ∫(x^x)^2(1+ x) d x equal to?

What is ∫ e^ x (1+ x+x x) d x equal to?

If I_1=∫ e^x d x e^x+e^ -x and I_2=∫ d x e^ 2 x +1 , then what is I_1+I_2 equal to?

What is ∫ ( x)^ 1.5 -( x)^ 1.5 x · x d x equal to?

What is ∫( x)^ -1 / 2 ( x)^ -3 / 2 d x equal to?

What is ∫ (d x)/(x(x^2+1)) equal to?

What is the integral of f(x)=1+x^2+x^4 with respect to x^2 ?

What is ∫ (d x)/( x+ x) equal to ?

If ∫ 1- 2 x d x=A x+B x+C , where 0 < x < (π)/(4) , then which one of the following is correct?

What is ∫ d x ^2( ^ -1 x) equal to ?

What is ∫ e^ (2 x+ x^2) d x equal to?

If p(x)=(4 e)^ 2 x , then what is ∫ p(x) d x equal to?

What is ∫(e^ x + x) x d x equal to ?

What is ∫ (d x)/(x(x^n+1)) equal to?

What is the value of k such that integration of (3 x^2+8-4 k)/(x) with respect to x , may be a rational function?

What is ∫ (d x)/(x(1+ x)^n) equal to (n^1 1) ?

What is ∫ (d x)/(2 x^2-2 x+1) equal to?

What is ∫ e^ x (a) d x equal to ?

What is ∫ (x^2) d x equal to ?

What is ∫ ^3 x x d x equal to? Where c is the constant o integration.

What is ∫ e^ In( x) d x equal to? Where c is the constant of integration.

What is ∫ d x a^2 ^2 x+b^2 ^2 x equal to?

What is ∫ dx 2^ x -1 equal to?

What is ∫ dx x(x^7+1) equal to?

What is ∫ ( ^ e-1 + ^ x-1 ) dx ^ e + ^ x equal to?

Let f(x) be an indefinite integral of ^2 x . Consider the following statements : Statement 1 : The function f(x) satisfies f(x+π)=f(x) for all real x. Statement 2: ^2(x+π)= ^2 x

What is ∫ ^ -1 ( x+ x) d x equal to?

∫(In x)^ -1 d x-∫(In x)^ -2 d x is equal to

What is ∫ x^4-1 x^2 x^4+x^2+1 d x equal to?

What is ∫ e^ x (x ^3 x- x)/( ^2 x) d x equal to?

Consider the function f(x)=(x-1)^2(x+1)(x-2)^3 . Let f(x) and g(x) be twice differentiable functions on [0,2] satisfying ^ (x)= ^ (x), ^ (1)=4, g^ (1)=6, f(2)=3 and g(2)=9 . Then

∫ dx 1+ ^ -x is equal to where c is the constant of integration

The integral ∫ (d x)/(a x+b x) is of the form (1)/(r) In [ ((x+α)/(2))]. What is r equal to?

What is ∫ d x x^2+a^2 equal to? where c is the constant of integration.

The integral ∫ (d x)/(a x+b x) is of the form (1)/(r) In [ ((x+α)/(2))]. What is to?

What is ∫ (x e^x d x)/((x+1)^2) equal to? where c is the constant integration.

Consider the function f^ (x)= ^4 x+4 with f(0)=0 and f^ (0)=0 . What is f^ (x) equal to?

Consider the function f^ (x)= ^4 x+4 with f(0)=0 and f^ (0)=0 . What is f(x) equal to?

Consider ∫ x ^ -1 x d x=A(x^2+1) ^ -1 x+B x+C , where C is the constant of integration. What is the value of A ?

Consider ∫ x ^ -1 x d x=A(x^2+1) ^ -1 x+B x+C , where C is the constant of integration. What is the value of B?

What is ∫ d x 4+x^2 equal to? where c is an arbitrary constant.

What is ∫(x x+ x) d x equal to? where c is an arbitrary constant.

What is ∫ ^2 x d x+∫ ^2 x d x equal to? where c is an arbitrary constant.

What is ∫ e^ e^x e^x d x equal to? where c is an arbitrary constant.

What is ∫ e^ x d x equal to? where c is constant of integration.

What is ∫ (d x)/(x x) equal to ? where c is the constant of integration.

What is ∫ a^x e^x d x equal to?

What is ∫ ( x)/(x) d x equal to?

What is ∫(x^2+1)^ (5)/(2) x d x equal to?

What is ∫((1)/( ^2 x)-(1)/( ^2 x)) d x equal to?

Consider the following: 1. ∫ 10 d x=x+c 2. ∫ 10^x d x=10^x+c where c is the constant of integration. Which of the above is/are correct?

What is ∫ (d x)/( ^2 x ^2 x) equal to? where c is the constant of integration.

What is ∫ x x d x equal to? where c is a constant of integration.

What is ∫ e^x( x + 1 2 x ) d x equal to? Where c is a constant of integration.

What is ∫ ^ -1 ( x) d x equal to? where k is a constant of integration.

What is equal to? ∫ (e^x(1+x))/( ^2(x e^x)) d x where c is a constant of integration.

What is ∫ ^n x x d x equal to? where c is a constant of integration.

If ∫ x^2 x d x=(x^2)/(m) x+(x^3)/(n)+c , then what are the values of m and n respectively? where c is a constant of integration.

What is ∫ (1)/(1+e^x) d x equal to? where c is constant of integration.

What is ∫ e^ x x d x equal to? where c is a constant of integration.

What is ∫ (x^4+1)/(x^2+1) d x equal to? where c is a constant of integration.

Consider the following statements: I. Every function has a primitive. II. A primitive of a function is unique. Which of the statements given above is/are correct?