Natural log cabin

Calculus Level 5

\[ \mathscr{E} = \displaystyle \int_{0}^{1} \ln(c) \ln(1-c) \, dc \]

If \( \mathscr{E} \) can be represented in the form \( a - \dfrac{\pi^{b}}{d} \), where \( a, b, d \) are positive integers, find \( a + b + d \).

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