It Takes Two

Calculus Level 4

\[\large I=\int_{0}^{1} \int_{0}^{1} \frac{1}{1-xy} \,dx\,dy\]

If \(\large \text{cis}(I)\) can be wirtten in the form \(\large a^{\frac{\pi}{b}}\) where \(\large a\) and \(\large b\) are integers. Find \(\large a+b\).

Note that \(\text{cis}(I)\) is the complex exponential function.

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