When will the holidays come 2

Calculus Level 4

\[\large \displaystyle\int_0^{\pi} x \sin^6(x) \cos^4(x) \, dx \]

If the integral above equals to \( \dfrac{a\pi^2}b \) where \(a\) and \(b\) are coprime integers, then find the value of \(\dfrac{a+b}{5}\).

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