# Working on a Difficult Integral

1. Aug 23, 2011

### Zoran

Hi All: I am working on a research project and am trying to get a symbolic solution to the following integral:

$$\int_{0}^{\frac{\pi }{4}}\int_{0}^{\frac{\pi }{4}}\frac{\cos\left ( z_{1} \right )\cos \left ( z_{2} \right )}{\sqrt{\left ( \cos\left ( z_{1} \right ) ^{2}+\frac{1}{2} \right )\left ( \cos\left ( z_{2} \right ) ^{2}+\frac{1}{2} \right )-\frac{1}{4}}}dz_{1}dz_{2}$$

The problem seems to be with the inclusion of the -1/4 in the denominator i.e. without it the integral has the solution:

$$\arctan\left ( \frac{1}{\sqrt{2}} \right ) ^{2}$$
.
Any help is appreciated.