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Integral of dx/(sqrt(d^2+x^2))

  1. Mar 30, 2012 #1
    Hi there. Evaluating the expression [itex]\int\frac{dx}{\sqrt{x^{2}+y^{2}}}[/itex] I can get to the result [itex]ln(\frac{x+\sqrt{x^{2}+y^{2}}}{d})[/itex], but in my book it goes from this directly to [itex]ln (x+\sqrt{x^{2}+y^{2}})[/itex], a result wolframalpha says is valid for 'restricted [itex]x[/itex] values'. What does it mean? What are those restricted values? Why?

    Many thanks.
  2. jcsd
  3. Mar 30, 2012 #2

    Well, since this is indefinite integration both the results are correct as their difference is just the constant [itex]-\ln d[/itex].

    The question is: where did you get the constant [itex]d[/itex] from??

    The result is valid for any values of [itex]x,y, s.t. x^2+y^2\neq 0[/itex]

  4. Mar 30, 2012 #3
    Thank you. 'd' is actually a constant length (the distance from a point p to a disk, in an axis that goes through the center of the disk)
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