Solution for cos^3 x dx.

PrudensOptimus

OK, I know the solution for cos^3 x dx is sinx - sin^3 x / 3 + C.


And that

you basically solve

integral of cosx*(1-sin^2x) dx. to get it.

but,...

what I don't get is how do you solve cosx*(1-sin^x) dx... is there a trick that I didn't get from the parts formula?

Hurkyl

It would help if you mentioned you're trying to integrate!

Distribute the multiplication and see if that gives you any hints.

HallsofIvy

Yes, one doesn't normally say "solve f(x)dx"!

Hurkyl, I don't see any reason to "distribute" (multiply out) anything. There is an obvious substitution for ∫(1- sin²(x))cos(x)dx.

Hurkyl

Good point. [:)]

PrudensOptimus

I have never learned integration by parts. Please help me.

Hurkyl

But, I presume, you know substitution?

PrudensOptimus

Nope, any products in Integrals other than those constants are new to me.

Hurkyl

I didn't ask about products, I asked about substitution!


E.G. would you know how to integrate ∫ sin(πx) dx

PrudensOptimus

i know the answer,

but I don't know the part when they did the dx = dv(ax) part... that confuzed me.

ShawnD

Ok well here's how I worked it out



I put a few steps together but you can still see what happened sort of.