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Solution for cos^3 x dx.

by PrudensOptimus
Tags: cos3, solution
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PrudensOptimus
#1
Nov4-03, 08:01 PM
P: 640
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?
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Hurkyl
#2
Nov4-03, 08:06 PM
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It would help if you mentioned you're trying to integrate!

Distribute the multiplication and see if that gives you any hints.
HallsofIvy
#3
Nov5-03, 06:53 AM
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Thanks
PF Gold
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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
#4
Nov5-03, 05:32 PM
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Solution for cos^3 x dx.

Good point.
PrudensOptimus
#5
Nov6-03, 06:40 PM
P: 640
I have never learned integration by parts. Please help me.
Hurkyl
#6
Nov6-03, 08:01 PM
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But, I presume, you know substitution?
PrudensOptimus
#7
Nov6-03, 08:31 PM
P: 640
Nope, any products in Integrals other than those constants are new to me.
Hurkyl
#8
Nov6-03, 08:33 PM
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I didn't ask about products, I asked about substitution!


E.G. would you know how to integrate ∫ sin(πx) dx
PrudensOptimus
#9
Nov6-03, 08:38 PM
P: 640
i know the answer,

but I don't know the part when they did the dx = dv(ax) part... that confuzed me.
ShawnD
#10
Nov7-03, 05:28 PM
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Ok well here's how I worked it out



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


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