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How the ? (Integration / Somewhat Urgent)

  1. May 5, 2009 #1
    1. Integrate on the interval [0, 1]: (x2 - 1)/(x2 + 1)

    2. No relevant equations.

    3.

    S x2/(x2 + 1) - [S 1/(x2 + 1)] =

    S (x2 + 1) - 1/(x2 + 1) - [(arctan x)] =

    S -1 - [(arctan x)] =

    -x - arctan x

    I can plug in the numbers on my own, but I would like to know if what I've done so far is correct...

    Thanks to anyone who reads this and answers it.

    - Lunar Guy
     
    Last edited: May 5, 2009
  2. jcsd
  3. May 5, 2009 #2
    How does ((x2 + 1) - 1)/(x2 + 1) become -1?
     
  4. May 5, 2009 #3

    a.a

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    the (x^2 + 1) cancles
    but where did u get x2/(x2 + 1) from?
    x^2 - 1 = x - 1)(x+1)
     
  5. May 5, 2009 #4
    The (x2 + 1) cancels to become 1 - (1/(x2 + 1)), not -1.
    He got x2/(x2 + 1) from (a + b)/c = a/c + b/c.
     
  6. May 5, 2009 #5

    a.a

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    so how does x^2/(x^2 +1) reduce to x^2 +1?
     
  7. May 5, 2009 #6
    That never happened. He skipped the step x2 = x2 + 1 - 1.
     
  8. May 5, 2009 #7
    Think its quite easy... Convert the neumerator in the form of the denominator by writing -1 as 1-2
     
  9. May 5, 2009 #8
    So now you get (xsquare + 1) - 2
     
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