How to integrate tan^2(x) sec^4(x)

 

$$\begin{array}{rl}& \int {\tan }^{2}x{\sec }^{4}xdx\\ & \text{ By Substitution }\\ & \begin{array}{c}\text{ Suppose }\begin{array}{rl}\Rightarrow z& =\tan x\\ dz& ={\sec }^{2}xdx\end{array}\\ \int z^2(1+z^2)\mathrm{d}z\\ \int z^2+z^{4}dz\end{array}\\ & \frac{z^3}{3}+\frac{z^5}{5}+c\\ & \frac{{\tan }^{3}x}{3}+\frac{{\tan }^{5}x}{5}+c\end{array}$$