# Solution for cos^3 x dx.

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?

## Answers and Replies

Hurkyl
Staff Emeritus
Science Advisor
Gold Member
It would help if you mentioned you're trying to integrate!

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

HallsofIvy
Science Advisor
Homework Helper
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 &int;(1- sin2(x))cos(x)dx.

Hurkyl
Staff Emeritus
Science Advisor
Gold Member
Good point.

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

Hurkyl
Staff Emeritus
Science Advisor
Gold Member
But, I presume, you know substitution?

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

Hurkyl
Staff Emeritus
Science Advisor
Gold Member
I didn't ask about products, I asked about substitution!

E.G. would you know how to integrate &int; sin(&pi;x) dx

i know the answer,

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

ShawnD
Science Advisor
Ok well here's how I worked it out

http://myfiles.dyndns.org/pictures/integrate1.jpg

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

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