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

  • Thread starter imurme8
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  • #1
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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...
 

Answers and Replies

  • #2
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What about the substitution [itex]x=u^2[/itex], followed by partial fraction decomposition?
 
  • #3
phyzguy
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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
 
  • #4
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Thanks guys!
 

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