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Math Help - integral of cos squared x sin x - substition guidance required

  1. #1
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    integral of cos squared x sin x - substition guidance required

    Hi

    I know that the answer to integral of cos^2 x sin x dx is -cos^3/3 but I am having trouble figuring out how the prof got there.

    Do you substitute u = cos x so du = -sin x? or do you substitute u = cos^2 x but then I am not sure what du =.

    Any guidance would be greatly appreciated.

    Thanks
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  2. #2
    A Plied Mathematician
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    In this case, you would do u=\cos(x), with du=-\sin(x)\,dx. What does

    \displaystyle\int\cos^{2}(x)\sin(x)\,dx become?
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  3. #3
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    it becomes integral -u^2 du which is -u^3/3 and then substitute back the cos x.

    Thank you very very very much. I just wasn't seeing before.
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  4. #4
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    Don't forget your constant of integration if it's an indefinite integral
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  5. #5
    A Plied Mathematician
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    That's right. You're welcome!

    P.S. Don't forget the constant of integration. Very important!
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