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: Integration help

  1. Mar 27, 2007 #1
    Greetings

    Can you help with the following integral:

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

    I'm reasonably sure my setup is correct up to this integral. I tried to factor and do some canceling. - no luck'

    thoughts and direction

    Thanks
    -Sparky-
     
    Last edited: Mar 27, 2007
  2. jcsd
  3. Mar 27, 2007 #2
    Have you tried substitution?
     
  4. Mar 27, 2007 #3

    ssd

    User Avatar

    Put, x^2+2x-1=z
     
  5. Mar 27, 2007 #4
    AHHH!! thanks -

    [tex] u = (1-2x-x^2) [/tex]
    [tex] du = -2 - 2x dx[/tex]
    [tex] dx = \frac {du} {-2(1+x)} [/tex]
    [tex] -\int \frac {-du} {u} [/tex]

    [tex] = ln(1-2x-x^2) [/tex]

    This solution is in the exponent of "e"

    and leads to the integral below.
    Question: can you suggest a start for:

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

    I've tried various substitutions again and don't see it.

    I've tried [tex] u = -x^2 - 2x [/tex]
    [tex] du = -2x - 2 dx [/tex]
    or
    [tex] (-2(x+1) )dx [/tex]
    [tex] dx = \frac {du} {-2(x+1)}[/tex]

    leaves me with a (x+1) term

    thanks
    Sparky_
     
    Last edited: Mar 27, 2007
  6. Mar 27, 2007 #5
    Note that [tex]1-2x-x^2 = -(x+1)^2 + 2[/tex].

    Now separate, and integrate.

    This is completing the square. Also you could multiply the bottom out and long divide to get a similar result.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook