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 :)

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- Oct 12th 2007, 11:47 PMUbikPkd[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 :)

- Oct 13th 2007, 12:01 AMticbol
- Oct 13th 2007, 12:04 AMDivideBy0
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 - Oct 13th 2007, 12:10 AMUbikPkd
thats great, thanks a lot! :)

- Oct 13th 2007, 12:33 AMDivideBy0
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.

- Oct 13th 2007, 12:42 AMUbikPkd
i had a feeling it wasn't gonna be simple....thanks anyway!