# Thread: Help wih Integration by Substitution

1. ## 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

2. 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.

3. What is $\displaystyle \dfrac{du}{dx} \text{ ?}$ (chain rule) - remember you can pull any constants out infront of the integral sign

4. 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)

5. Originally Posted by mm874
Is e^(2x) not just 2e^(2x)?

u= e^(2x)+1

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

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

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