# Thread: Another trig integral

1. ## Another trig integral

Hey y'all,

Ok, I'm stuck on another one:

$\displaystyle \int (tan(x))^3 sec(x) dx$

I usually try to take out one of the tan x and then do my u substitution with the sec x, but my du would be tanxsecx which would leave me with a sec x left over with my du. How should I tackle this one?

Thanks!!

2. Originally Posted by mollymcf2009
Hey y'all,

Ok, I'm stuck on another one:

$\displaystyle \int (tan(x))^3 sec(x) dx$

I usually try to take out one of the tan x and then do my u substitution with the sec x, but my du would be tanxsecx which would leave me with a sec x left over with my du. How should I tackle this one?

Thanks!!
Note that $\displaystyle \tan^3 x \sec x = \tan x \tan^2 x \sec x = \tan x (\sec^2 x - 1) \sec x = (\sec^2 x - 1) \sec x \tan x$

now do you see it?