Question

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

Answer 1

I already looked at Wolfram and I don't want to use the reduction formula

Answer 2

Sin*(Sin^2(x))

Answer 3

Then:
Sin*(1-Cos^2(x))

Answer 4

That leads to
Sin - Sin*Cos^2
split it into two integrals

Answer 5

first one is easy, second one - integration by parts, then you go through the loop again

Answer 6

I say reduction formula I think it's 1/2 something... is much easier

Answer 7

ok I see what you want to do

Answer 8

I've never been taught that reduction formula so I'd rather not use it yet

Answer 9

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..

Answer 10

yeah that makes sense
I'll try it using your strategy

Answer 11

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!

Answer 12

yes, subbing for the second part is way easier, it's practically udu already because it is cos^n(x)*(-sinx)