# Tricky Integral

1. Aug 9, 2014

### FeynmanIsCool

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!

$\int_{0}^{\frac{\pi }{2}}\, \frac{1}{1+(tanx)^{\sqrt 2}} dx$

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. Aug 9, 2014

### Jorriss

This is an integral from one of the old putnams, if you google around you can probably find it.

Consider the substitution of $$\frac{\pi}{2} - x$$ into $$f(x) = \frac{1}{1+tan^{\sqrt(2)}(x)}$$ This gives $$f(π/2 - x) = 1-f(x)$$ 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
3. Aug 15, 2014