Question

intrigate sin^6x

Answer 1

You would have to use power-reduction formula multiple times and work it out. Not sure theres an easier way. But the power reduction formula for sin is
\[\sin^{2}x = \frac{ 1-\cos2x }{ 2 }\]So for you, you would need to do that, but it would be cubed. Doing it 3 times youd have to solve this:

\[\sin^{6}x = (\frac{ 1-\cos2x }{ 2 })^{3}\]

Answer 2

you can also repeatedly use the reduction formula\[\int\sin^nxdx={-\sin^{n-1}x\cos x\over n}+{n-1\over n}\int\sin^{n-2}xdx\] but it's not much easier