# Definite Integral of a Trig Fxn

π/3
∫tan^5 x sec x
0

I want to split the tan^5 x into a (sec^2 x - 1) but I only have sec x. So I'm a bit stuck. Help is appreciated.

ehild
Homework Helper
Bring the integral in the form ∫f(cos(x))sin(x)dx.

ehild

SammyS
Staff Emeritus
Homework Helper
Gold Member
π/3
∫tan^5 x sec x
0

I want to split the tan^5 x into a (sec^2 x - 1) but I only have sec x. So I'm a bit stuck. Help is appreciated.
Finding the anti-derivative of tan5(x) sec(x) is a lot like solving your previous tread.

Split tan5(x) into tan4(x) tan(x) then use the trig identity which will change tan4(x)  into a combination of secant functions.

^ That did the trick. Thank you : D