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Integrate (cosx)(sinx)^3

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    I've tried splitting it up into (cosx)(sinx)(sinx)^2, and then using various identities, but that's really long-winded. The shortness of the other questions in the exercise leads me to believe that there is a better way?

    HALP
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    Substitution perhaps?
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    u=sinx
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    cos x is the derivative of sin x, so this is simply a reverse chain rule job, surely?
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    Because sinx differentiates to cosx, you just integrate (sinx)^3 to get ((sinx)^4)/4
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    It's not that long-winded is it?
    but yeah, just do a simple substitution.

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Updated: February 2, 2010
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