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Finding the indefinite integral of sin^2(pi*x) cos^5(pi*x)

  1. Feb 19, 2016 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    Just the above.

    3. The attempt at a solution
    I have no idea how pi effects the answer, so I basically solved ∫(sin2(x)^cos5(x))dx.

    u = sin x du = -cos x dx

    ∫(u2*(1-u2)2) -du
    -∫(u2*(1-u2)2) du
    -∫(u2*(1-2u2+u4) du
    -∫(u2-2u4+u6) du


    When I look up what the antiderivative should be on integral-calculator.com. the minus sign outside of the parentheses disappears, which I can't figure out how.

    Can anyone give me some help?
  2. jcsd
  3. Feb 19, 2016 #2


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    Homework Helper

    If u = sin x then du = cos x, not - cos x.
  4. Feb 19, 2016 #3


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    Science Advisor
    Homework Helper
    Gold Member

    Fix the sign error that RUber pointed out. Then do the original problem the same way but let ##u =\sin(\pi x)##.
    [Edit:] Fixed typo.
    Last edited: Feb 19, 2016
  5. Feb 19, 2016 #4


    Staff: Mentor

    No doubt just an oversight, but du = cos(x) dx.
  6. Feb 29, 2016 #5
    Thanks everyone. Figured it out.
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