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Math Help - Help wih Integration by Substitution

  1. #1
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    Help wih Integration by Substitution

    I am trying to integrate the following using u-substitution:

    ∫e^(2x)/(e^(2x)+1)^(1/2)

    Where u=e^(2x)+1

    I am stuck and am not sure where to go with this. Can someone walk me through the steps so I can finish my revision.

    Thanks

    Matt
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  2. #2
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    Just in case a picture helps, here's one I made earlier with 3 instead of minus a half (and 4 instead of ...?) ...



    at here.


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    Don't integrate - balloontegrate!

    Standard Integrals, Derivatives and Methods.
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  3. #3
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    What is \dfrac{du}{dx} \text{ ?} (chain rule) - remember you can pull any constants out infront of the integral sign
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  4. #4
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    Is e^(2x) not just 2e^(2x)?

    u= e^(2x)+1

    du/dx = 2e^(2x)

    now how do I write it in the terms if du.

    So far i would have e^2/u^(3/2)/(3/2)
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  5. #5
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by mm874 View Post
    Is e^(2x) not just 2e^(2x)?

    u= e^(2x)+1

    du/dx = 2e^(2x)
    Correct. Also multiplying through by dx du = 2e^{2x} dx.

    Note that you have e^{2x}dx in the numerator so you may sub in du here: 2e^{2x}dx = 2\, du


    \displaystyle 2\int \dfrac{du}{u^{1/2}} = 2 \int u^{-1/2}du
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