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JEE Main 2025 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 7 April 2025, Shift 2, Maths Q24

Question 24 of 75 in this shift, Maths question 24 of 25, Section B.

If

\int\left(\frac{1}{x}+\frac{1}{x^3}\right)\sqrt[23]{3x^{-24}+x^{-26}}\,dx=-\frac{\alpha}{3(\alpha+1)}\left(3x^{\beta}+x^{\gamma}\right)^{\frac{\alpha+1}{\alpha}}+C

,

x>0

,

(\alpha,\beta,\gamma\in\mathbf{Z})

, where

C

is the constant of integration, then

\alpha+\beta+\gamma

is equal to ________.

Official answer

19

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Factoring Highest Power for Substitution

Same idea in other shifts

Asked 3× in all

26 Jun 2022, Shift 2 · Q28The integral $\frac{24}{\pi}\int_0^{\sqrt{2}} \frac{(2 - x^2)\,dx}{(2 + x^2)\sqrt{4 + x^4}}$ is equal to ______.HardNumerical value
8 Jan 2020, Shift 1 · Q60If $\int\dfrac{\cos x\,dx}{\sin^3 x\,(1+\sin^6 x)^{2/3}}=f(x)\,(1+\sin^6 x)^{1/\lambda}+c$ where c is a constant of integration, then…HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.