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JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 August 2021, Shift 2, Maths Q69

Question 69 of 90 in this shift, Maths question 9 of 30, Section A.

If

\int\sin^{-1}\left(\frac{2x+2}{\sqrt{4x^2+8x+13}}\right)dx=A\tan^{-1}\left(\frac{2x+2}{3}\right)+B\log_e\left(4x^2+8x+13\right)+C

(C is a constant of integration), then the ordered pair (A, 4B) is equal to

(1) $\left(\frac{3}{2}(x+1),-3\right)$
(2) $\left(\frac{3}{2}(x+1),3\right)$
(3) $(x+1,-3)$ Official answer
(4) $(x+1,-6)$

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Integration by Parts
Idea tested: Inverse Trig Simplification Before Parts

Same idea in other shifts

Asked 2× in all

3 Sep 2020, Shift 2 · Q60If $\int \sin^{-1}\left(\sqrt{\frac{x}{1+x}}\right) dx = A(x)\tan^{-1}(\sqrt{x}) + B(x) + C$ , 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.