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Solution for cos^3 x dx.

  1. Nov 4, 2003 #1
    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?
     
  2. jcsd
  3. Nov 4, 2003 #2

    Hurkyl

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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.
     
  4. Nov 5, 2003 #3

    HallsofIvy

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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.
     
  5. Nov 5, 2003 #4

    Hurkyl

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    Good point. :smile:
     
  6. Nov 6, 2003 #5
    I have never learned integration by parts. Please help me.
     
  7. Nov 6, 2003 #6

    Hurkyl

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    But, I presume, you know substitution?
     
  8. Nov 6, 2003 #7
    Nope, any products in Integrals other than those constants are new to me.
     
  9. Nov 6, 2003 #8

    Hurkyl

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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
     
  10. Nov 6, 2003 #9
    i know the answer,

    but I don't know the part when they did the dx = dv(ax) part... that confuzed me.
     
  11. Nov 7, 2003 #10

    ShawnD

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    Ok well here's how I worked it out

    [​IMG]

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