1. Limited time only! Sign up for a free 30min personal 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!

Having trouble with the antiderivative of this function

  1. Apr 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Evaluate the indefinite integral:
    [tex]\int[/tex]7x+1/x^2+1 dx


    2. Relevant equations



    3. The attempt at a solution
    My first attempt at the solution was to try using substitution. I set u=x^2+1. so du=2x dx and x=sqrt(u-1). Then I rewrote the integral so it is [tex]\int[/tex]7du/4usqrt(u-1). This is where I don't know where to go with this attempt.

    I'm pretty sure I'm going about this problem all wrong. If I could just get a push in the right direction I'd really appreciate it :)
     
  2. jcsd
  3. Apr 8, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Split the integral into 7x/(x^2+1) and 1/(x^2+1). The first one is the u-substitution you spoke of. The second is a trig substitution.
     
  4. Apr 8, 2009 #3
    Thank you very much. So the first one becomes [tex]\int[/tex]7/2u du then 7/2ln(x^2+1) after taking the anti derivative and substituting x^2+1 for u. Then the second part becomes arctan x. So would the final answer be (7/2)ln(x^2+1)+arctan(x)?
     
  5. Apr 8, 2009 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That looks fine to me.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook