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

Published On :2021-01-27 11:52:00

[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}]