JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 18 March 2021, Shift 1, Maths Q73

Question 73 of 90 in this shift, Maths question 13 of 30, Section A.

The 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)

(1) $\frac{1}{2}\sin\sqrt{(2x+1)^2+5}+c$
(2) $\frac{1}{2}\sin\sqrt{(2x-1)^2+5}+c$ Official answer
(3) $\frac{1}{2}\cos\sqrt{(2x-1)^2+5}+c$
(4) $\frac{1}{2}\cos\sqrt{(2x+1)^2+5}+c$

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 5× in all

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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.