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Calculus Level 4

$\large \displaystyle \int_{0}^{{\pi} / {4}}\cos^{10}x\sin{20x} \, dx$

If the integral above is of the form $$\dfrac A B$$, where $$A$$ and $$B$$ are coprime positive integers, find $$A+B$$.

Note: Mathematical as well as Programming solution is acceptable.

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