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Prove integral

  1. Dec 31, 2009 #1
    [tex]\int \frac{dx}{(1+x^2)^n} \;=\; \frac{1}{2(n-1)}\cdot\frac{x}{(1+x^2)^{n-1}}
    \;\;-\;\; \frac{2n-3}{2(n-1)}\int \frac{dx}{(1+x^2)^{n-1}}[/tex]

    Can someone prove this?
     
  2. jcsd
  3. Dec 31, 2009 #2

    berkeman

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    Staff: Mentor

    What is the context of your question? Is it for schoolwork/homework?
     
  4. Dec 31, 2009 #3
    I have exam (university) January 15th and we have exercises but we don't have answers.. so I would lik to know how to solve this one
     
  5. Dec 31, 2009 #4

    berkeman

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    Staff: Mentor

    Okay. Schoolwork needs to go in the Homework Help forums, and you need to show some effort on trying to solve it. I'll move the thread now. Can you say anything about potential ways to solve the problem?
     
  6. Dec 31, 2009 #5
  7. Dec 31, 2009 #6
    Have you try [tex]x=tan(\theta)[/tex]

    [tex]1+tan^{2}(\theta)=sec^{2}(\theta)[/tex]
     
    Last edited: Dec 31, 2009
  8. Jan 1, 2010 #7
    I think you made a mistake typing it: It should be '+' in between the 2 fraction and the integral.

    Just do a simple Integration by parts without induction.

    Let dv=dx , u = 1/(1+x2)n

    In = x/(1+x2)n + 2n(integral)[x2/(1+x2)n+1]dx

    as 'x2 = 1 + x2 - 1',

    You should end up with: In = x/(1+x2)n + 2n(In - In+1)

    Make In+1 the subject. Finally lower each of the n terms by 1. (so n+1 -> n, and n -> n-1)
     
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