Random Points On A Square

Calculus Level 5

A square with a unit length has two arbitrary points chosen inside it. What is the average distance between the two points?

If this can be represented in the form \(\dfrac {a + \sqrt{b} + c \ln (d+\sqrt{e})}{f}\), where \(a, b, c, d, e, f\) are positive integers, and the fraction is simplified as far as possible, find \(a+b+c+d+e+f\).

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