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$\int \frac{1}{\cos x(1+\cos x)} d x=$
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Verified Answer
The correct answer is:
$\log (\sec x+\tan x)-\tan \frac{x}{2}+c$
$\begin{aligned} \int \frac{1}{\cos x(1+\cos x)} d x & =\int \frac{d x}{\cos x}-\int \frac{d x}{1+\cos x} \\ & =\int \sec x d x-\frac{1}{2} \int \sec ^2 \frac{x}{2} d x \\ & =\log (\sec x+\tan x)-\tan \frac{x}{2}+c .\end{aligned}$
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