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!

Trig Identity Integral

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data
    I missed one class on trigonometric identities in integrals, and I feel that one is needed here:

    [itex]\int^3_0\frac{1+arctan(\frac{x}{3})}{9+x^2}dx[/itex]


    2. Relevant equations



    3. The attempt at a solution
    Again, I'm unsure what to do. I think that it is a trig identity, but I could be wrong. I'll continue to try parts & substitutions..

    Thanks!
     
  2. jcsd
  3. Oct 18, 2011 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The derivative of acrtan(x) is 1/(x2+1), so the derivative of acrtan(x/3) is 3/(x2+9)
     
  4. Oct 18, 2011 #3

    Mark44

    Staff: Mentor

    Split the integral into two integrals. The first can be done directly and the second can be done with an ordinary substitution. Integration by parts is not the way to go.

    Do you know this differentiation formula?
    [tex]\frac{d}{dx} tan^{-1}(x)?[/tex]
     
  5. Oct 18, 2011 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Notice that [itex]\displaystyle \frac{d((f(x)^2)}{dx}=2f(x)f'(x)\,.[/itex]

    That does that imply regarding [itex]\displaystyle \int\ f(x)f\,'(x)\,dx\,?[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook