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How does one integrate a quotient?

  1. Oct 21, 2012 #1
    How do you integrate quotients? Let's practice with one like... [tex]\int\frac{3x + x^{2}}{5x - 1} dx[/tex]

    Thanks for the help!
     
    Last edited by a moderator: Oct 21, 2012
  2. jcsd
  3. Oct 21, 2012 #2

    Mark44

    Staff: Mentor

    Is this homework?
     
  4. Oct 21, 2012 #3
    No, I just pulled that one out of thin air. This will help me with homework in the future, but right now, that is just an example.
     
  5. Oct 21, 2012 #4

    Mark44

    Staff: Mentor

    I would use polynomial long division to write the integrand as a polynomial plus a remainder term that is a proper rational expression. If you don't know this technique, do a search on wikipedia for "polynomial long division."
     
  6. Oct 22, 2012 #5
    Another method : change of variable
    t=5x-1
    Rewrite the integral with t and dt (witout x nor dx in it)
     
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