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## Homework Statement

∫(e

^{x})/(2e

^{x}+2)dx

## Homework Equations

and I am told to use:

u=2e

^{x}+2

## The Attempt at a Solution

If i use u=2e

^{x}+2 as the task says;

du/dx = 2e

^{x}and dx =du/2e

^{x}

∫(e

^{x})/(u)du/2e

^{x}=∫(1)/(2u)du=1/2ln|u| + c =1/2ln|2e

^{x}+2|

according to the book the answer should be 1/2ln|e

^{x}+1|

however if i use u =e

^{x}+1 and write the integral 1/2∫(e

^{x})/(e

^{x}+1)dx i get the correct answer. Where am i going wrong?

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