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Tricky Integral

  1. Aug 9, 2014 #1
    Hello everyone,

    I brushing up on integration techniques and I came across this problem in a book. Does anyone here know were to start? Even Wolfram blanked on it!

    [itex]\int_{0}^{\frac{\pi }{2}}\, \frac{1}{1+(tanx)^{\sqrt 2}} dx[/itex]

    This integral appeared in the book before sequences and series, so the book did not intend to use any type of series expansion.

    Let me know!
  2. jcsd
  3. Aug 9, 2014 #2
    This is an integral from one of the old putnams, if you google around you can probably find it.

    Consider the substitution of [tex] \frac{\pi}{2} - x [/tex] into [tex]f(x) = \frac{1}{1+tan^{\sqrt(2)}(x)}[/tex] This gives [tex] f(π/2 - x) = 1-f(x) [/tex] Now, break the integral up into two parts, one from 0 to pi/4 and the other from pi/4 to pi/2 and manipulate the second integral using the above identity.
    Last edited: Aug 9, 2014
  4. Aug 15, 2014 #3
    Thanks for the reply,

    You're right, I found the answer quickly after a google search. Very interesting integral!
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