Fifty shades of integration?

Calculus Level 5

01x2(1x)4ln(1x)dx \large \displaystyle \large \int_{0}^{1} x^{2} (1-x)^4 \ln \left(\frac{1}{x}\right ) \, dx

If the value of the integral above is equal to ab \dfrac ab, where aa and bb are coprime positive integers, find a+ba+b.

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