JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 16 March 2021, Shift 2, Maths Q81

Question 81 of 90 in this shift, Maths question 21 of 30, Section B.

For real numbers

\alpha,\beta,\gamma

and

\delta

, if

\int\frac{(x^2-1)+\tan^{-1}\left(\frac{x^2+1}{x}\right)}{(x^4+3x^2+1)\tan^{-1}\left(\frac{x^2+1}{x}\right)}dx=\alpha\log_e\left(\tan^{-1}\left(\frac{x^2+1}{x}\right)\right)+\beta\tan^{-1}\left(\frac{\gamma(x^2-1)}{x}\right)+\delta\tan^{-1}\left(\frac{x^2+1}{x}\right)+C

where C is an arbitrary constant, then the value of

10(\alpha+\beta\gamma+\delta)

is equal to ________.

Official answer

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Composite Function Substitution

Same idea in other shifts

Asked 5× in all

3 Apr 2025, Shift 1 · Q18Let $f(x) = \int x^3\sqrt{3 - x^2}\,dx$ . If $5f(\sqrt{2}) = -4$ , then $f(1)$ is equal toMediumSingle correct
30 Jan 2024, Shift 2 · Q12Let $y = f(x)$ be a thrice differentiable function in $(-5, 5)$ . Let the tangents to the curve $y = f(x)$ at $(1, f(1))$ and $(3, f(3))$ …HardSingle correct
30 Jan 2024, Shift 2 · Q13Let $f: \mathbb{R} \to \mathbb{R}$ be a function defined by $f(x) = \frac{x}{(1+x^4)^{1/4}}$ , and $g(x) = f(f(f(f(x))))$ . Then,…HardSingle correct
18 Mar 2021, Shift 1 · Q73The integral $\int\dfrac{(2x-1)\cos\sqrt{(2x-1)^2+5}}{\sqrt{4x^2-4x+6}}\,dx$ is equal to : (where c is a constant of integration)MediumSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.