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How does my book get from this step to this step?

  1. Oct 6, 2007 #1
    [SOLVED] How does my book get from this step to this step?

    My book went from int of dx/ ( sqrt(x)*(x+1) )

    to

    2arctan sqrt (x) -- WTH?

    I thought the form for arctan was dx/a^2 + u^2 and I don't see that in the given integrand?

    Can anyone help?
     
  2. jcsd
  3. Oct 6, 2007 #2

    arildno

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    Substitute [tex]u=\sqrt{x}[/tex], and see what you get.
     
  4. Oct 6, 2007 #3

    Astronuc

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    If x=u2, then dx = 2 u du

    sqrt (x) = u, and

    x+1 = u2 + 1
     
  5. Oct 6, 2007 #4
    astronuc, did you arrive at that by using the substitution arildno suggested?
     
  6. Oct 6, 2007 #5

    HallsofIvy

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    Well, arildno said "u= [itex]\sqrt{x}[/itex]" and Astronuc said "x= u2". Look the same to me!
     
  7. Oct 6, 2007 #6
    Ha, you rascal!
     
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