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The integral \(\int\left(\frac{x}{x \sin x+\cos x}\right)^2 d x\) is equal to (where \(C\) is a constant of integration)…

Q1

The integral \(\int\left(\frac{x}{x \sin x+\cos x}\right)^2 d x\) is equal to (where \(C\) is a constant of integration):

[JEE Main 2020, 4 Sep (Shift 1)]

a

\(\tan x-\frac{x\sec x}{x\sin x+\cos x}+C\)

b

\(\sec x-\frac{x\tan x}{x\sin x+\cos x}+C\)

c

\(\tan x+\frac{x\sec x}{x\sin x+\cos x}+C\)

d

\(\sec x+\frac{x\tan x}{x\sin x+\cos x}+C\)

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