Question

"Evaluate
∫sin^6(x)cos^3(x)dx." I just keep going in circles, can anyone help?

Answer 1

look in the back of your book the "power reduction formulas" and you will see them

Answer 2

since the power of cosine is odd, you can use
\[u=\sin(x), du=\cos(x)dx\] and \(\cos^2(x)=1-\sin^2(x)\)to get
\[\int u^6(1-u^2)du\]

Answer 3

had some technical difficulties but thank you. I don't remember learning anything about power reduction so I'll go figure that out now that I know where to start