# Degrees of Definite Integral

Calculus Level 5

$\large I= \int_0^\pi x^3\ln\sin x\, dx\\\large k = \int_0^\pi x^2\ln\left(\sqrt2\sin x\right)\,dx$

Let the two integrals be defined as given above. If $$I$$ can be written as $$I = \dfrac{A\pi^B}C k$$, where $$A$$, $$B$$ and $$C$$ are positive integers with $$A$$ and $$C$$ being coprime integers. Find $$A+B+C$$.

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