# Integration-problem using u-substitution

∫(ex)/(2ex+2)dx

## Homework Equations

and im told to use:

u=2ex+2

## The Attempt at a Solution

If i use u=2ex+2 as the task says;

du/dx = 2ex and dx =du/2ex

∫(ex)/(u)du/2ex=∫(1)/(2u)du=1/2ln|u| + c =1/2ln|2ex+2|

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

however if i use u =ex+1 and write the integral 1/2∫(ex)/(ex+1)dx i get the correct answer. Where am i going wrong?

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