Where did digamma come from?

Calculus Level 5

\[\large \int _{ 0 }^{ 1 }{ \dfrac { (1-{ x }^{ 2 })\ln { x } }{ 1-{ x }^{ 3 } } \, dx } =\dfrac { { \pi }^{ a } }{ b } -\dfrac { \psi ^{ (1) }(1/c) }{ d } \]

If the above equation holds true for positive integers \(a,b,c\) and \(d\), find \(a+b+c+d\).

Notation: \(\psi^{(1)}(\cdot) \) denotes the first derivative of the digamma function.

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