JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 18 March 2021, Shift 1, Maths Q83

Question 83 of 90 in this shift, Maths question 23 of 30, Section B.

f(x)=\int\dfrac{5x^8+7x^6}{(x^2+1+2x^7)^2}\,dx

(x\ge0)

f(0)=0

and

f(1)=\dfrac{1}{K}

, then the value of K is __________.

Official answer

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Quotient Rule Differential Recognition

Same topic in other shifts

All Integration by Substitution questions

5 Apr 2026, Shift 1 · Q20The value of the integral $\int_{\pi/6}^{\pi/3}\left(\frac{4 - \operatorname{cosec}^2 x}{\cos^4 x}\right)dx$ is:MediumSingle correct
5 Apr 2026, Shift 2 · Q18Let $(2^{1-a}+2^{1+a})$ , $f(a)$ , $(3^a+3^{-a})$ be in A.P. and $\alpha$ be the minimum value of $f(a)$ . Then the value of the integral…HardSingle correct
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
4 Apr 2025, Shift 2 · Q25If…HardNumerical value
7 Apr 2025, Shift 2 · Q24If…HardNumerical value
6 Apr 2024, Shift 2 · Q12If $\int\frac{1}{a^2\sin^2x+b^2\cos^2x}dx=\frac{1}{12}\tan^{-1}(3\tan x)+\text{constant}$ , then the maximum value of $a\sin x+b\cos x$ , is :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.