# Integration-problem using u-substitution

1. Oct 8, 2013

### johann1301

1. The problem statement, all variables and given/known data

∫(ex)/(2ex+2)dx

2. Relevant equations

and im told to use:

u=2ex+2

3. 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?

Last edited: Oct 8, 2013
2. Oct 8, 2013

### BruceW

they are both correct, the only difference is the constant of integration, which you don't know anyway. Hint: write 2ex+2 as a constant times ex+1, and then make use of the properties of logarithms to see that you get the same answer (without caring about the constant of integration, since you don't know it anyway).