Another trig integral

**mollymcf2009** · February 5th 2009, 08:42 PM

Hey y'all,

Ok, I'm stuck on another one:

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

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!!

**Jhevon** · February 5th 2009, 08:50 PM

Originally Posted by mollymcf2009

Hey y'all,

Ok, I'm stuck on another one:

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

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 $\tan^3 x \sec x = \tan x \tan^2 x \sec x = \tan x (\sec^2 x - 1) \sec x = (\sec^2 x - 1) \sec x \tan x$

now do you see it?

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