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Solution for cos^3 x dx. 
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#1
Nov403, 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*(1sin^2x) dx. to get it. but,... what I don't get is how do you solve cosx*(1sin^x) dx... is there a trick that I didn't get from the parts formula? 


#2
Nov403, 08:06 PM

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Sci Advisor
PF Gold
P: 16,091

It would help if you mentioned you're trying to integrate!
Distribute the multiplication and see if that gives you any hints. 


#3
Nov503, 06:53 AM

Math
Emeritus
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Thanks
PF Gold
P: 39,553

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 sin^{2}(x))cos(x)dx. 


#5
Nov603, 06:40 PM

P: 640

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



#7
Nov603, 08:31 PM

P: 640

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



#8
Nov603, 08:33 PM

Emeritus
Sci Advisor
PF Gold
P: 16,091

I didn't ask about products, I asked about substitution!
E.G. would you know how to integrate ∫ sin(πx) dx 


#9
Nov603, 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. 


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