Possibly the strangest calculus problem?

Calculus Level 5

n=101xn1ln2(x)ln(1x)n2dx=πab \sum_{n=1}^\infty\int_0^1 \frac{x^{n-1}\ln^2(x)\ln(1-x)}{n^2} \,dx=-\frac{\pi^{\large a}}{b}

Find a+b\,\large a+b\, for the following problem

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