# How to integrate this conundrum?

1. Mar 30, 2012

### I<3Gauss

Does anyone know how to prove the following statement? I haven't messed with integrals for awhile and I have to say that I am kind of rusty on this. From initial attempts, it seems the integral on the left is not something you can integrate directly.... Maybe Taylor Expansion of cos^2(x) would help?

∫x/(1+cos^2(x)) = pi/(2*√2) (integrated from pi to 0)

Thanks guys!

2. Mar 30, 2012

### Whovian

So you're asking for $$\displaystyle\int\limits_0^\pi\left(\dfrac{x\cdot dx}{1+\cos^2\left(x\right)}\right)$$? My first thought was substitute $$u=\dfrac\pi2-x$$ and doing something like averaging out the results. Anyone?

EDIT: GRRR ... why isn't there a \mathrm on here?

3. Mar 30, 2012

### I<3Gauss

Whovian, What gave you the idea to make such a substitution? What technique are you using?

4. Mar 30, 2012

### Whovian

It's just a substitution that helps with a lot of trig integrals from 0 to pi/2.