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Math Help - Substitution

  1. #1
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    Substitution



    A friend gave me this procedure, but I'm in doubt with something. Can someone tell me how they got the values for u, dv, du, and v?

    Thanks
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  2. #2
    MHF Contributor
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    Google L.I.A.T.E, but this is less important than seeing why the choice of u and v that works works. Which is about working backwards through the product rule. Just in case a picture helps...



    ... where (key in spoiler) ...

    Spoiler:


    ... is the product rule.Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x).



    ... is lazy integration by parts, doing without u and v.



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  3. #3
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    Thanks tom!
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