When will the holidays come 2

Calculus Level 4

0πxsin6(x)cos4(x)dx\large \displaystyle\int_0^{\pi} x \sin^6(x) \cos^4(x) \, dx

If the integral above equals to aπ2b \dfrac{a\pi^2}b where aa and bb are coprime integers, then find the value of a+b5\dfrac{a+b}{5}.

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