\[\begin{equation} \begin{aligned} &\int \tan ^{2} x \sec ^{4} x d x\\ &\text { By Substitution }\\ &\begin{array}{l} \text { Suppose } \begin{aligned} \Rightarrow z &=\tan x \\ d z &=\sec ^{2} x d x \end{aligned} \\ \int z^{2}\left(1+z^{2}\right) \mathrm{d} z \\ \int z^{2}+z^{4} d z \end{array}\\ &\frac{z^{3}}{3}+\frac{z^{5}}{5}+c\\ &\frac{\tan ^{3} x}{3}+\frac{\tan ^{5} x}{5}+c \end{aligned} \end{equation}\]
Tags:
integration