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Integration-problem using u-substitution

  • Thread starter johann1301
  • Start date
  • #1
217
1

Homework Statement



∫(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?
 
Last edited:

Answers and Replies

  • #2
BruceW
Homework Helper
3,611
119
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).
 

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