Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Tricky Integral
  1. Tricky integral (Replies: 2)

  2. Integration Trickiness (Replies: 6)

  3. Tricky integral (Replies: 3)

  4. Tricky integral ? (Replies: 10)

  5. A tricky integral (Replies: 1)

Loading...