Help with a integration problem (trigonometric substitution)
I'm having a test on integration on Monday and I'm having some major problems with solving integrations involving trigonometric substitution. There's a sample of a problem I'm having issues with:
This is where I get stuck. I remember my teacher saying that I have to get everything in terms of u before I go substituting u back into the equation, however, I don't see a feasible way to do this. If someone could step my through this one so I can see how it's done, I'd really appreciate it.
I = Integration symbol
u = dummy variable for substitution
I tan^2(6x) * dx
I ---------- * dx u = cos(6x)
cos^2(6x) du = -6sin(6x) * dx
dx = ------------
I ---------- * --------
--- I -------- * du
If you all need any more information about the problem or something I'll do my best to provide. Regards.