ILATE or LIATE? (Nineteenth integral)

Calculus Level 5

\[ \displaystyle \int_{0}^{1} \arcsin(x) \ln(x) \, dx \]

If the above integral can be expressed in the form

\[ a - \dfrac{b \pi}{c} - \ln d \],

where \(a, b, c, d \) are positive integers and \( b, c \) are coprime, find \(a+b+c+d \).

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