How do you integrate (sin(x))^3 ?

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How do you integrate (sin(x))^3 ?

Mathematics
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I already looked at Wolfram and I don't want to use the reduction formula
Sin*(Sin^2(x))
Then: Sin*(1-Cos^2(x))

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That leads to Sin - Sin*Cos^2 split it into two integrals
first one is easy, second one - integration by parts, then you go through the loop again
I say reduction formula I think it's 1/2 something... is much easier
ok I see what you want to do
I've never been taught that reduction formula so I'd rather not use it yet
remember that? Then at the end you get something like Int(Sin*Cos^2) = __________ - Int(Sin*Cos^2), then u add Int(Sin*Cos^2) to both sides and divide by two or whatever..
yeah that makes sense I'll try it using your strategy
I ended up using subsitution for the second part because it seemed easier I got (((cos(x))^3)/3) - cos(x) Thanks again for your help!
yes, subbing for the second part is way easier, it's practically udu already because it is cos^n(x)*(-sinx)

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