Roaring Integral!

Calculus Level 4

0π1(53cosx)3dx=απβ\large \displaystyle \int_{0}^{\pi} \dfrac{1}{(5-3\cos x)^3}\, dx = \dfrac{\alpha \pi}{\beta}

In the above integral, if α\alpha and β\beta are coprime positive integers, then find α+β\alpha + \beta .

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