JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 September 2020, Shift 1, Maths Q61

Question 61 of 75 in this shift, Maths question 11 of 25.

The integral

\int \left(\frac{x}{x\sin x + \cos x}\right)^2 \mathrm{d}x

is equal to (where C is a constant of integration) :

(1) $\sec x + \frac{x\tan x}{x\sin x + \cos x} + C$
(2) $\sec x - \frac{x\tan x}{x\sin x + \cos x} + C$
(3) $\tan x + \frac{x\sec x}{x\sin x + \cos x} + C$
(4) $\tan x - \frac{x\sec x}{x\sin x + \cos x} + C$ Official answer

Official answer

Option 4

NTA final key (Sep 2020).

Chapter: Integrals
Topic: Integration by Parts
Idea tested: Integrability over ILATE

Same topic in other shifts

All Integration by Parts questions

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11 Apr 2023, Shift 1 · Q26For $m, n > 0$ , let $\alpha(m, n) = \int_0^2 t^m(1+3t)^n\,dt$ . If $11\,\alpha(10, 6) + 18\,\alpha(11, 5) = p\,(14)^6$ , then $p$ is equal…HardNumerical value

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.