# Trig integral

1. Mar 2, 2008

### grothem

1. The problem statement, all variables and given/known data
$$\int tan^5(6x) sec^3(6x) dx$$

2. Relevant equations

3. The attempt at a solution
first off I set u=6x to get 1/6$$\int tan^5(u) sec^3(u) dx$$
then I used trig identities to put tangent in terms of secant and I came up with

$$\int sec^9(u)-3sec^7(u)+3sec^5(u)-sec^3(u) dx$$
Not sure where to go from here, or if I'm doing this the right way
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 2, 2008

### rocomath

$$\frac 1 6\int\tan^{5}u\sec^{3}udu$$
$$\frac 1 6\int\tan^{4}u\sec^{2}\sec u\tan udu$$
*$$\tan^{2}u+1=\sec^{2}u$$