Integration strategy?

  • Thread starter demersal
  • Start date
  • #1
41
0

Homework Statement


[tex]\int[/tex][tex]\frac{\frac{1}{3}x+\frac{2}{3}}{x^{2}-x+1}[/tex]


Homework Equations



This is the result of a partial fraction integration. I don't think a direct u-substitution will work or an integration by parts.

The Attempt at a Solution



I don't know which I should use! We learned so many and none seem to work nicely in this case. Should I try to do a trigonometric substitution? That is my best guess, but since there is no radical I have no idea how to implement it!

Any sort of hint would be great. I'm just not "seeing it" ;)
 
Last edited:

Answers and Replies

  • #2
Defennder
Homework Helper
2,591
5
Complete the square of the denominator then break it up using (a+b)(a-b) = a^2 - b^2. From here you can do it by partial fractions, though it appears tedious.
 

Related Threads on Integration strategy?

  • Last Post
Replies
3
Views
904
  • Last Post
Replies
0
Views
951
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
3K
Replies
3
Views
2K
Replies
1
Views
1K
  • Last Post
Replies
4
Views
2K
Replies
6
Views
1K
Top