Question

What is `int tan^3(x)*sec(x)dx`?

Answer 1

`=(sec^3 x)/3-sec x+C`

Explanation:

By rewriting a bit,

`int tan^3 x sec x dx=int tan^2 x cdot secx tan x dx=int(sec^2 x-1)sec x tan x dx`

By substitution `u=sec x`, `Rightarrow du = sec x tan x dx`,

#=int(u^2-1)du =u^3/3-u+C =(sec^3 x)/3-sec x+C#

I hope that this was clear.