Integration-problem using u-substitution

[johann1301]

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?

 

[BruceW]

they are both correct, the only difference is the constant of integration, which you don't know anyway. Hint: write 2e^x+2 as a constant times e^x+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).