Question

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

• A. $\frac{1}{2+\tan x} + c$
• B. $-\frac{1}{2\tan x+1} + c$
• C. $\frac{\cos x}{\cos x+2\sin x} + c$
• D. $\frac{\cos x}{2\cos x + \sin x} + c$

Hint:

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.

Answer 1

The Correct Option is D