Challenging Definite Integral with Square Roots and Logarithms

[lordy2010]

Homework Statement

Evaluate integral from -1 to 1 of: sqrt(ln(6-x))/(sqrt(ln(6-x))+sqrt(ln(6+x)))

Homework Equations

n/a

The Attempt at a Solution

I barely know how to approach this integral. I've been trying to figure this out for a long time now, and I feel like I haven't gotten anywhere. I have even used Wolfram Alpha to take a look at the function and it looks like a straight line between -1 and 1. The answer is also, apparently, 1.

Thank you in advanced for the help!

 

[timthereaper]

Think about using the properties of logs:

ln(xy)=ln(x)+ln(y)
ln(x/y)=ln(x)-ln(y)

 

[lordy2010]

I have considered the properties of logs and, if there were no square roots surrounding each of the ln terms, then I would have an idea of what to do. Unfortunately, there are the square roots outside of the logs so I'm still pretty lost with this integral. :-/