Evaluate the indefinite integral.

Question

∫ sec^3x tanx dx

I let u=tanx
took derivative..
du=sec^2x dx

..now what??

Answer 1

sec^3 x tan x dx
| = integral symbol

Rewrite as
| sec^2 x sec x tan x dx
u = sec x
du = sec x tan x

| u^2 du
1/3 u^3 + C

Substitute back in, u = sec x
1/3 sec^3 x + C