How do anti-differentiate this?

integral of (sin^3 x)

I'm pretty sure this is wrong, but I got "-x + (cos^3x)/3"

Actually fuck that shit, I just worked it out and you don't need integration by parts

all you have to do, if it is actually sin^3(x)
is break it into sin(x)*sin^2(x) and then use power reduction on the sin^2(x) which becomes (1 -cos(2x))/2 or some shit and then the integration is very basic