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Math Help - Help identifying substitution value for integral

  1. #1
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    Help identifying substitution value for integral

    The question:
    Use a substitution to evaluate \int x(5x -1)^{19} dx

    My attempt:
    Normally I'd check to see if value within the brackets is an anti-derivative of the element outside (chain rule). In this case, it isn't. I'm uncertain as to how I should go about finding a substitution. Any ideas? Thanks.
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  2. #2
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    Quote Originally Posted by Glitch View Post
    The question:
    Use a substitution to evaluate \int x(5x -1)^{19} dx

    My attempt:
    Normally I'd check to see if value within the brackets is an anti-derivative of the element outside (chain rule). In this case, it isn't. I'm uncertain as to how I should go about finding a substitution. Any ideas? Thanks.
    \displaystyle\ u=5x-1\Rightarrow\ \frac{du}{dx}=5\Rightarrow\ \frac{du}{5}=dx

    \displaystyle\frac{u+1}{5}=x

    \displaystyle\int{x(5x-1)^{19}dx=\int{\frac{u+1}{5}u^{19}\frac{du}{5}=\fr  ac{1}{25}\int{(u+1)u^{19}}du=\frac{1}{25}\int{\lef  t(u^{20}+u^{19}\right)}du
    Last edited by Archie Meade; October 26th 2010 at 08:13 AM.
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  3. #3
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    I really need to get better at spotting these tricks! Thanks!
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  4. #4
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    response edited.
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  5. #5
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    Hehe, thanks. I went to do it myself and noticed you made an error. :P
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