Question

\[\int\limits_{}^{}\tan^3x secx dx \]

Answer 1

first, change tan^3 x = tan^2x tanx

Answer 2

I tried this

\[\int\limits_{}^{}(\tan^2x. tanx. secx) dx \]
\[\int\limits_{}^{}(\sec^2x-1) (tanx. secx) dx \]

Answer 3

Yeah, continue with that and set u = sec x
du = sec x tan x

Answer 4

du = sec x tan x dx

Answer 5

ok, then multiply of them by use distributive property
= int (sec^2x secxtanx - secxtanx) dx
= int (sec^2x secxtanx) dx - int (secxtanx) dx

Answer 6

case I :
int (sec^2x secxtanx) dx
use int by subs, like slaaibak said : u=secx
case II :
int (secxtanx) = secx (i sure u have remembered) :p

Answer 7

I think I do :)

thanks @RadEn and @slaaibak