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!

Homework Help: An integration involving inverse trig.

  1. Dec 29, 2009 #1
    1. The problem statement, all variables and given/known data

    The question is integrate

    [tex]\int_0^1 (2+\frac{1}{x+1}+\frac{2x+1}{x^2+4}) dx[/tex]

    2. Relevant equations

    [tex]\int_0^1 (2+\frac{1}{x+1}+\frac{2x+1}{x^2+4}) dx =2 + ln(\frac{5}{2}) +\frac{1}{2}arctan(\frac{1}{2})[/tex] (yes, it's a prove question)

    3. The attempt at a solution

    The first two parts I have no problem but I am not quite sure how to integrate the

    [tex]\frac{2x+1}{x^2+4}[/tex] part. I know it has to do with arctan but I'm not quite sure about the [tex]2x+1[/tex] part.

    Thanks in advance,
  2. jcsd
  3. Dec 29, 2009 #2
    Split up the last fraction so that you have [tex]\frac{2x}{x^{2}+4} + \frac{1}{x^{2}+4}[/tex]. Use a simple substitution for the first fraction and then the second fraction will involve the inverse tangent. In general,

    [tex]\int \frac{dx}{x^2+a^2} = \frac{1}{a} arctan(\frac{x}{a}) + C[/tex]
  4. Dec 29, 2009 #3
    ahh! I completely missed that step! Thanks for your help :)

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook