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Integrate: 1/(1+2x+x^2) dx

  1. Jul 8, 2004 #1
    In an exam i stumbled when i saw this q
    integrate:
    1/(1+2x+x^2) dx
    :grumpy:
    help
     
  2. jcsd
  3. Jul 8, 2004 #2
    [tex]\int \frac{dx}{1+2x+x^2}[/tex]

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

    Whats the pro
     
  4. Jul 9, 2004 #3
    ?????
    ?????
     
  5. Jul 9, 2004 #4
    [tex] 1 + x^2[/tex] + [tex]\frac{1}{3}x^3[/tex]
     
    Last edited: Jul 9, 2004
  6. Jul 9, 2004 #5
    Substitute [itex]u=x+1[/itex]. [itex]du=dx[/itex] so we get

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

    That should make it a little easier to see what rule you can apply.
     
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