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An analytic solution?

  1. Apr 7, 2010 #1
    Is there an analytic solution to the following integral? (Not a homework question, solved numerically).

    [tex]\int_{0}^{\infty}{\frac{dx}{(1+x)\sqrt{x}}=\pi[/tex]
     
  2. jcsd
  3. Apr 7, 2010 #2
    Let u^2 = x
     
  4. Apr 8, 2010 #3
    OK I get: [tex]2\int\frac{1}{1+u^2}du[/tex]

    I'm a bit rusty at this. I think I need to make some trig substitutions here, but I'm at a loss as to exactly what.
     
    Last edited: Apr 8, 2010
  5. Apr 8, 2010 #4
    It's just there, the arc tangent.
     
  6. Apr 8, 2010 #5
    Right. I finally saw that. However, the solution: [tex]2\arctan(\sqrt{x})+C[/tex] contains a variable. The solution given in the CRC Standard Mathematical Tables 14th ed, page 342, Eq 489 is [tex]\pi[/tex].

    EDIT:Yes, I know it's old, but I doubt a new solution has been invented. I bought it for $2.
     
    Last edited: Apr 8, 2010
  7. Apr 8, 2010 #6

    D H

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    You looked up the indefinite integral. You have a definite integral. Apply the integration limits.
     
  8. Apr 8, 2010 #7
    The form of the integral in the book is just as I wrote it in the first post, but I see how the solution [tex]\pi[/tex] is obtained. Thanks.
     
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