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Math Help - Integration query

  1. #1
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    Integration query

    Integral of cos(^3)2x
    i did - cos2x X cos(^2)2x
    Then changed cos(^2)2x to 1-sin(^2)2x
    How do i proceed now?
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  2. #2
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    The derivative of \sin^2(2x) is 4\sin(2x)\cos(2x).
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  3. #3
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    Yes ok, i substituted that.what do i do next?
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  4. #4
    A Plied Mathematician
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    I would probably do a u substitution from your \cos(2x)(1-\sin^{2}(2x)): u=\sin(2x).
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  5. #5
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    Yes,the substitution worked.Thanks
    But is there also any other way to do it?
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  6. #6
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    Yes.

    \cos3{\theta} = 4\cos^3{\theta} - 3\cos{\theta}

    From the above equation find cos^3(x) and then find the integration.
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