# Homework Help: Powers or Trig Functions Question - Integral

1. Jun 18, 2008

### Shkolnikoff

1. The problem statement, all variables and given/known data
Integral of : (sec x)^5 (tan x)^3 dx

2. Relevant equations
I am having trouble substituting correctly for this equation and i cant get it to work. I believe it has to do with trig powers ?

If anyone could help be step by step. or even just a hint on how to solve it that would be great.

Thanks in advance !
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jun 18, 2008

### Gib Z

Welcome to PF!

My Hint would be to rewrite the tan cubed term in terms of a square and a linear, then change the square term with a Pythagorean identity, expand and see where that takes you.

Last edited: Jun 18, 2008
3. Jun 18, 2008

### konthelion

You should probably memorize this rule for integrating trigonometric integrals

For any $$\int{tan^{m}xsec^{n}xdx}$$

If n is even, substitute u = tan(x)
If m is odd, substitute u = sec(x)
If m is even, n is odd, reduce to powers* of sec(x)
Also, using the identity $$1+tan^{2}x=sec^{2}x$$ is helpful in all three cases

Last edited: Jun 18, 2008
4. Jun 18, 2008

### Shkolnikoff

Thank you very much for all your help. I just finished solving the problem.

Its alot easier using the hints you provided! Thanks!