1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problem integrating

  1. May 11, 2009 #1
    I'm supposed to integrate w/w^4 + 1

    The two ideas I'd come up with was trying to substitute w^4+1 with u but that results in a 0 in the numerator.

    Then I thought maybe I have to put w/w^4+1 into the 1/1+w^2 form and integrate into 1/k tan^-1kx + C but I'm not sure how to keep the original function while making the w^4 a w^2.

    Help please? Am I at least going in the right direction with any of these ideas?
     
  2. jcsd
  3. May 11, 2009 #2

    dx

    User Avatar
    Homework Helper
    Gold Member

    Use integration by parts. You'll have to do it twice.

    EDIT: Mark44's way is better, ignore this.
     
  4. May 11, 2009 #3

    Mark44

    Staff: Mentor

    You're going in the right direction thinking of tan-1(x).

    An ordinary substitution should do the trick: u = x2, so du = 2xdx. Then your integrand becomes roughly du/(u2 + 1). Notice the parentheses I added to make clear what the denominator is. You'll also need to add the right constant multiplier in the numerator, since I omitted it.
     
  5. May 11, 2009 #4
    Does that mean I can substitute just the variable and leave the "+ 1"? That is substitute u as w^2 getting u^2 = u^4?
     
  6. May 11, 2009 #5

    dx

    User Avatar
    Homework Helper
    Gold Member

    You mean u2 = w4.
     
  7. May 11, 2009 #6

    Mark44

    Staff: Mentor

    Yes. The substitution is u = w2, so u2 = w4, and du = 2wdw.
     
  8. May 11, 2009 #7
    Oh, yeah. Typo. That's what I meant.

    Awesome, thanks for the help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Problem integrating
  1. Integration problem (Replies: 4)

  2. Integral Problem (Replies: 31)

  3. Integration problem (Replies: 9)

  4. Integration Problem (Replies: 7)

Loading...