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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