Right track

  • Thread starter Airsteve0
  • Start date
  • #1
83
0

Main Question or Discussion Point

Hey everyone, I was wondering if someone could help me understand what exactly is happening with a certain integral I am working with, which is as follows:

∫2/(u^2-1)du

My steps are as follows (I used partial fractions):

∫(1/(u-1) - 1/(u+1))du = ∫1/(u-1)du - ∫1/(u+1) = ln[(u-1)/(u+1)]

However, here is where my issue arrises; when checking my answer with Mathematica, if I input the very first line above I get:

ln[(1-u)/(1+u)]

Could someone help me understand if it is my method that is flawed or maybe the way I am inputting it into the program when I check my answer. Any assistance is greatly appreciated, thanks!
 

Answers and Replies

  • #2
993
13
ln[(u-1)/(u+1)] = ln[(-1 +u)/(1+u)] = ln[(-1)(1-u)/(1+u)] =ln(-1) + ln[(1-u)/(1+u)] .

Since the integral is indefinite, there must be a constant of integration. The ln(-1) can be incorporated in this constant.

So if you add a constant to your solution, your answer and that given by Matematica will be equivalent.
 
  • #3
lurflurf
Homework Helper
2,426
126
Both answers are correct as they differ by a constant.
 
  • #4
83
0
o ok so the constant can be complex in general then?
 
  • #5
lurflurf
Homework Helper
2,426
126
Yes the constant would be complex. To avoid dealing with this often absolute values are used since otherwise the function would be undefined. In fact different constants are needed in different ranges.
 
  • #6
83
0
thank you very much for the clarification and assistance!
 

Related Threads for: Right track

  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
1K
Replies
2
Views
2K
Replies
4
Views
2K
Replies
2
Views
607
Top