Natural log integral

Calculus Level 4

The value of integral\[\int_{0}^{1} \ln(x) \ln(1-x) \ \text{d} x\] can be written as \[a-\frac{\pi^{b}}{c}\] where \(a\), \(b\) and \(c\) are positive integers. Find \(a+b+c\).

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