$\underset{0}{\overset{\pi /4}{\int }}\left({\tan }^{4}x+{\tan }^{2}x\right)dx$

$\begin{array}{l}\text{ G.I }={\int }_0^{\pi /4} \left({\tan }^{2}x+1\right){\tan }^{2}xdx\\ ={\int }_0^{\pi /4} {\tan }^{2}x\cdot {\sec }^{2}xdx\\ ={\left[\frac{{\tan }^{3}x}{3}\right]}_0^{\pi /4}=\frac{1}{3}=0.3330\end{array}$