Indefinite Integrals — JEE Main Previous Year Questions

How many JEE Main questions come from Indefinite Integrals?

Indefinite Integrals has contributed 81 questions to Joint Entrance Examination (Main) papers between 2016 and 2026 — an average of about 7 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 81 questions carries a written, step-by-step solution, and each is tagged to Indefinite Integrals within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Indefinite Integrals questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 81 Indefinite Integrals questions (with full written solutions) are available in practice.

1. Question 1 · JEE Main 2026

   Let $f(x)=\int \frac{\left(2-x^2\right)\cdot {\mathrm{e}}^x}{(\sqrt{1+x})(1-x{)}^{3/2}}\mathrm{d}x$. If $f(0)=0$, then $f\left(\frac{1}{2}\right)$ is equal to:
   1. (A)$\sqrt{2\mathrm{e}}-1$
   2. (B)$\sqrt{2\mathrm{e}}+1$
   3. (C)$\sqrt{3\mathrm{e}}-1$
   4. (D)$\sqrt{3\mathrm{e}}+1$
   Show answerAnswer

   Answer: (C) $\sqrt{3\mathrm{e}}-1$

2. Question 2 · JEE Main 2026

   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 :
   1. (A)$-5$
   2. (B)$-11$
   3. (C)$-18$
   4. (D)$-26$
   Show answerAnswer

   Answer: (B) $-11$

3. Question 3 · JEE Main 2026

   If $\int \left(\frac{1-5{\cos }^{2}x}{{\sin }^{5}x{\cos }^{2}x}\right)dx=f(x)+\mathrm{C}$, where C is the constant of integration, then $f\left(\frac{\pi }{6}\right)-f\left(\frac{\pi }{4}\right)$ is equal to
   1. (A)$\frac{1}{\sqrt{3}}(26-\sqrt{3})$
   2. (B)$\frac{4}{\sqrt{3}}(8-\sqrt{6})$
   3. (C)$\frac{1}{\sqrt{3}}(26+\sqrt{3})$
   4. (D)$\frac{2}{\sqrt{3}}(4+\sqrt{6})$
   Show answerAnswer

   Answer: (B) $\frac{4}{\sqrt{3}}(8-\sqrt{6})$

4. Question 4 · JEE Main 2026

   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 :
   1. (A)31
   2. (B)37
   3. (C)39
   4. (D)41
   Show answerAnswer

   Answer: (C) 39

5. Question 5 · JEE Main 2026

   Let $f(t)=\int \left(\frac{1-\sin \left({\log }_{e}t\right)}{1-\cos \left({\log }_{e}t\right)}\right)dt,t>1$. If $f\left(e^{\pi /2}\right)=-e^{\pi /2}$ and $f\left(e^{\pi /4}\right)=\alpha e^{\pi /4}$, then $\alpha$ equals
   1. (A)$1+\sqrt{2}$
   2. (B)$-1-2\sqrt{2}$
   3. (C)$-1-\sqrt{2}$
   4. (D)$-1+\sqrt{2}$
   Show answerAnswer

   Answer: (C) $-1-\sqrt{2}$

Indefinite Integrals questions by year

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