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!

Fun problem: ? x / (x^2 + 6x + 10) dx

  1. Mar 17, 2004 #1
    Fun problem: ? x / (x^2 + 6x + 10) dx

    Integration by parts proves 1=1! My mathematical fame is at hand! So how would you do this one?
     
  2. jcsd
  3. Mar 18, 2004 #2
    [tex]\int\frac{x}{x^2 + 6x + 10}{\rm d}x = \frac12\left(\ln[10 + x(6 + x)]-6 \arctan [3 + x] \right)[/tex]


    So, what does this have to do with 1=1 (which is selfevidently true anyway)?
     
    Last edited: Mar 18, 2004
  4. Mar 18, 2004 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Integration by parts proves 1=1? In other words, you used integration by parts twice, the second time reversing your choice for u and dv so the two cancelled!

    "Partial fractions" is what you need here. The denominator, x^2 + 6x + 10, is "irreducible" over the real numbers. It is the same as
    x^2+ 6x+ 9+ 1= (x+3)^2+ 1. I would recommend the substitution
    u= x+ 3 so that du= dx, x= u- 3 and the problem becomes integrating
    (u-3)/(u^2+1)= u/(u^2+1)- 3/(u^2+1).

    The first of those can be done by the further substitution v= u^2+1 and the second is a simple arctangent.
     
  5. Mar 18, 2004 #4
    OOops, I forgot that x could be expressed in terms of u.
     
    Last edited: Mar 19, 2004
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?