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Integral of x^{-1/2}*(1-x)^-1

  1. Jan 27, 2013 #1
    Claim: [itex]\int\frac{dx}{\sqrt{x}(1-x)}=\log{\frac{1+\sqrt{x}}{1-\sqrt{x}}}[/itex]
    Derivation confirms this, but how was this answer arrived at? IBP seems not to work, can't find a good u-substitution...
  2. jcsd
  3. Jan 27, 2013 #2
    What about the substitution [itex]x=u^2[/itex], followed by partial fraction decomposition?
  4. Jan 27, 2013 #3


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    Try writing:

    [tex]\frac{1}{\sqrt{x}(1-x)} = \frac{1}{\sqrt{x}(1+\sqrt{x})(1-\sqrt{x})}[/tex]

    then use a u substitution and partial fractions
  5. Jan 27, 2013 #4
    Thanks guys!
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