Question:medium

$\int \frac{1}{(2\cos x + \sin x)^2} dx =$

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When faced with a complicated integral, especially in a multiple-choice format, consider differentiating the given options. If the derivative of an option matches the integrand (or is a constant multiple of it), you have found the answer. Be aware of potential sign errors in the question or options.

Updated On: Mar 30, 2026

$\frac{1}{2+\tan x} + c$
$-\frac{1}{2\tan x+1} + c$
$\frac{\cos x}{\cos x+2\sin x} + c$
$\frac{\cos x}{2\cos x + \sin x} + c$

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The Correct Option is D

Solution and Explanation

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