Integrating tan^5(6x) sec^3(6x) - A Guide

[grothem]

Homework Statement

$$\int tan^5(6x) sec^3(6x) dx$$

Homework Equations

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

 

[rocomath]

Watch your substitutions.

$$\frac 1 6\int\tan^{5}u\sec^{3}udu$$

$$\frac 1 6\int\tan^{4}u\sec^{2}\sec u\tan udu$$

*$$\tan^{2}u+1=\sec^{2}u$$

Take it from here.