JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int \frac{x^2+n(n-1)}{(x \sin x+n \cos x)^2} d x

is equal to

View answer and explanation

Correct option: D

\frac{-x^n \sec x}{x^n \sin x+n x^{n-1} \cos x}+\tan x+c

Option B (

\frac{{-\sec x}}{{x \sin x+n \cos x}}+\tan x+c

) is incorrect. Option D (

\frac{{-x^n \sec x}}{{x^n \sin x+n x^{n-1} \cos x}}+\tan x+c

) is the correct answer because after integration by parts and simplification, the expression matches this form.

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