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Trigonometric Integral Help please!

  1. Jun 8, 2012 #1
    1. The problem statement, all variables and given/known data
    ∫sin^3xcos^63xdx


    2. Relevant equations



    3. The attempt at a solution
    ∫sin^3xcos^63xdxsin^3xcos^63xdx

    let u=cosx
    du=-sinxdx
    -du=sinxdx

    =∫sin^2xcos^63xsinxdx
    =∫(1-cos^2x)cos^63x-du
    =-∫(1-u^2)u^63du
    =-∫(u^63-u^65)du
    =-u^64/64-u^66/66+c
    =(-cos^64x/64)-(cos^66x/66)+c

    ^ I'm thinking this is not the correct answer?
     
  2. jcsd
  3. Jun 8, 2012 #2

    vela

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    Try differentiating it and see if you recover the integrand.
     
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