Definite Integral of a Trig Fxn

[johnhuntsman]

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]

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

ehild

 

[SammyS]

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.

 

[johnhuntsman]

^ That did the trick. Thank you : D