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JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 3 September 2020, Shift 2, Maths Q60

Question 60 of 75 in this shift, Maths question 10 of 25.

If

\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 the ordered pair

(A(x), B(x))

can be :

(1) $(x + 1, -\sqrt{x})$ Official answer
(2) $(x + 1, \sqrt{x})$
(3) $(x - 1, -\sqrt{x})$
(4) $(x - 1, \sqrt{x})$

Official answer

Option 1

NTA final key (Sep 2020).

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

Same idea in other shifts

Asked 2× in all

4 Aug 2021, Shift 2 · Q69If $\int\sin^{-1}\left(\frac{2x+2}{\sqrt{4x^2+8x+13}}\right)dx=A\tan^{-1}\left(\frac{2x+2}{3}\right)+B\log_e\left(4x^2+8x+13\right)+C$ (C…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 108 of the 174 JEE Main shifts held from 2017 to 2026.