TITLE: Integral question - $\int\frac{\sqrt{\tan(x)}}{{\cos^2(x)}}dx$
QUESTION [0 upvotes]: Integral question - $$\int\frac{\sqrt{\tan(x)}}{{\cos^2(x)}}dx$$
I see that $\frac{1}{\cos^2(x)}$ is the derivative of $\tan(x)$ so I set $t =  \tan(x)$? or the whole square?

Thanks!

REPLY [1 votes]: Hint: for a derivable function $\,f(x)\,$ , we have that
$$\int\sqrt{f(x)}\;f'(x)\;dx=\frac23f(x)\sqrt{f(x)} + C$$
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