Đáp án:
$\begin{array}{l}
\int\limits_0^{\pi /4} {\frac{{\sqrt {\tan x} }}{{co{s^2}x}}dx} \\
= \int\limits_0^{\pi /4} {\sqrt {\tan x} .d\left( {\tan x} \right)} \\
= \int\limits_0^{\pi /4} {{{\tan }^{\frac{1}{2}}}x.d\left( {\tan x} \right)} \\
= \frac{2}{3}.\tan x.\sqrt {\tan x} _0^{\pi /4}\\
= \frac{2}{3}
\end{array}$