# integral of cos squared x sin x - substition guidance required

• Apr 5th 2011, 10:26 AM
calcbeg
integral of cos squared x sin x - substition guidance required
Hi

I know that the answer to integral of cos^2 x sin x dx is -cos^3/3 but I am having trouble figuring out how the prof got there.

Do you substitute u = cos x so du = -sin x? or do you substitute u = cos^2 x but then I am not sure what du =.

Any guidance would be greatly appreciated.

Thanks
• Apr 5th 2011, 10:29 AM
Ackbeet
In this case, you would do $\displaystyle u=\cos(x),$ with $\displaystyle du=-\sin(x)\,dx.$ What does

$\displaystyle \displaystyle\int\cos^{2}(x)\sin(x)\,dx$ become?
• Apr 5th 2011, 10:32 AM
calcbeg
it becomes integral -u^2 du which is -u^3/3 and then substitute back the cos x.

Thank you very very very much. I just wasn't seeing before.
• Apr 5th 2011, 10:34 AM
e^(i*pi)
Don't forget your constant of integration if it's an indefinite integral (Wink)
• Apr 5th 2011, 10:34 AM
Ackbeet
That's right. You're welcome!

P.S. Don't forget the constant of integration. Very important!