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Math Help - Integral

  1. #1
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    Integral

    I need help with an Integral.

    It is:

    2(sin2x)^3... so I set u to 2x and du to 2 so this would make he integral of

    du(sinu)^3... now I'm stuck

    Thanks
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  2. #2
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    Quote Originally Posted by alex.caine View Post
    I need help with an Integral.

    It is:

    2(sin2x)^3... so I set u to 2x and du to 2 so this would make he integral of

    du(sinu)^3... now I'm stuck

    Thanks
    \int\sin^3u\,du

    =\int\sin u\sin^2 u\,du

    =\int\sin u(1-\cos^2u)\,du

    =\int\sin u\,du-\int\sin u\cos^2u\,du

    Can you handle it from here?
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  3. #3
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    \int 2\sin^3(2x)dx = \int 2\sin(2x)(1-\cos^2(2x))
    =\int2\sin(2x)-2\sin(2x)\cos^2(2x)
    =-\cos(2x)-\cos^3(2x) (differentiate to check)

    Works for all odd-powered trig integrals.
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