Thread: [SOLVED] Integral of cos squared x

so using


which is all fine and dandy (i think) but what's the integral of ?

is there a better way of doing it?

Also what would be or and

i guess im looking for a general rule of and

thanks in advance

Originally Posted by UbikPkd

so using


which is all fine and dandy (i think) but what's the integral of ?

thanks in advance

INT.[sin^2(X)cosX]dX
= INT.[sin^2(X)]cosX dX

if u were sinX, then du = cosX dX, so

= (1/3)sin^3(X) +C

I personally would use u-substitution. Notice that is the derivative of , so it works nicely.

Let , then

So that turns the integral into



Now substituting back into u:



(Didn't see u post ticbol) :P

thats great, thanks a lot!

Unfortunately there is no easy generalisation for nth powers, you have to use reduction formulas. Here are some of them. You could try to derive them using integration by parts, if you've learnt that.

i had a feeling it wasn't gonna be simple....thanks anyway!