A calculus problem by Refaat M. Sayed

Calculus Level 5

\[\large \int^{{\pi } /{2} }_{0}\tan ^{3}( x) \cos ^{5}(x) \cos (7x) \, dx=\dfrac{A}{B} \]

The equation above holds true for some coprime positive integers \(A\) and \(B\). Find \(A+B\).


Bonus: Find the close form of the definite integral, \[I_{Y,Z} = \int ^{{\pi } / {2} }_{0}\left( \tan \left( x\right) \right) ^{Y}\left( \cos \left( x\right) \right) ^{Z-2}\cos \left( Zx\right) \, dx\]

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