Integrate with sin cos #2

Calculus Level 5

\[\large{\displaystyle \int^{\frac{\pi}{4}}_{0} (\sin 2 \theta)^{\frac{5}{2}} (\sin \theta+\cos \theta) \, d\theta=\frac{A}{B} \pi}\]

If \(A\) and \(B\) are coprime integers, find \(A+B\).

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