Indefinite Integrals JEE Main PYQs (2020–2026)

Solved Indefinite Integrals PYQs

3 recent questions with answers. The full set of 54 is free to practise.

1. JEE Main 2026EasyStandard Elementary Integrals & Direct Integration
   Q1

   Let $f(x)=\int \left(\frac{16x+24}{x^2+2x-15}\right)dx$ . If $f(4)=14{\log }_e(3)$ and $f(7)={\log }_e(2^{\alpha }\cdot 3^{\beta })$ , $\alpha ,\beta \in \mathbb{N}$ , then $\alpha +\beta$ is equal to :

   • A31
   • B37
   • C39
   • D41

   Show answer & solution

   Correct answer: (C)

   JEE Main 2026 (Online) 2nd April Evening Shift
2. JEE Main 2026EasyIntegration by Substitution
   Q2

   Let $f(x)=\int \frac{dx}{x^{2/3}+2x^{1/2}},$ be such that $f(0)=-26+24{\log }_e(2)$ . If $f(1)=a+b{\log }_e(3)$ , where $a,b\in \mathbb{Z}$ , then $a+b$ is equal to :

   • A$-5$
   • B$-11$
   • C$-18$
   • D$-26$

   Show answer & solution

   Correct answer: (B)

   JEE Main 2026 (Online) 28th January Evening Shift
3. JEE Main 2026HardIntegration by Parts
   Q3

   If $\int \left(\frac{1-5{\cos }^{2}x}{{\sin }^{5}x{\cos }^{2}x}\right)dx=f(x)+C$ , where C is the constant of integration, then $f\left(\frac{\pi }{6}\right)-f\left(\frac{\pi }{4}\right)$ is equal to

   • A$\frac{1}{\sqrt{3}}(26-\sqrt{3})$
   • B$\frac{4}{\sqrt{3}}(8-\sqrt{6})$
   • C$\frac{1}{\sqrt{3}}(26+\sqrt{3})$
   • D$\frac{2}{\sqrt{3}}(4+\sqrt{6})$

   Show answer & solution

   Correct answer: (B)

   JEE Main 2026 (Online) 28th January Morning Shift

Topic-wise question count

Where JEE Main has asked from Indefinite Integrals, most frequent first.

• Integration by Substitution26
• Special Quadratic Integrals (1/(ax^2+bx+c), etc.)8
• Integration by Parts6
• Integration using Partial Fractions4
• Integrals of the form (px+q)/sqrt(ax^2+bx+c)3
• Standard Elementary Integrals & Direct Integration2
• Integrals of Rational Functions of sin x and cos x2
• Integration using Trigonometric Identities2

Year-wise Indefinite Integrals questions in JEE Main

Number of questions from this chapter in each year's paper(s).