Question

What is integral of `tan^2(x) sec^4(x) dx?`

Answer 1

Another way of seeing this problem

`I = inttan^2(x)sec^4(x)dx`
`= inttan^2(x)(1+tan^2(x))^2dx`
`u = tan(x)` then `dx = (du)/(1+u^2)`
`=int(u^2(1+u^2)^2/(1+u^2))du`
`=int(u^2+u^4)du`
`=u^3/3+u^5/5+C`
`I=tan^3(x)/3+tan^5(x)/5+C`