Integral of tan³(πx)dx using substitution

[Arjun571]

Homework Statement

Integral of Tan^3(PiX)dx

Homework Equations

The Attempt at a Solution

Int= Integral
PI=22/7
Int Tan^3(22/7X)dx
=Int Tan(22/7X)Tan^2(22/7X)dx
=Int (Sec^2(22/7X)-1)(Tan(22/7X)dx
=Int (Tan(22/7X)Sec^2(22/7X)-Tan(22/7X)dx
=...?
Im lost as to where to go from here, should i use a U substitution for one of them?

 

[rock.freak667]

Split the integral as two integrals now.

so you have

∫tan(πx) sec²(πx) dx - ∫ tan(πx) dx

for the first integral, you can use u=tan(πx) and for the second one, rewrite tan as sin/cos.

 

[Arjun571]

oooh, i don't know how i didnt seen that before, thanks a lot man

 

[dextercioby]

$$I = \int \tan^3 x \, dx = - \int d\cos x \, \frac{1-\cos^2 x}{\cos^3 x} = ...$$