A calculus problem by Refaat M. Sayed

Calculus Level 5

0π/2tan3(x)cos5(x)cos(7x)dx=AB\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 AA and BB. Find A+BA+B.


Bonus: Find the close form of the definite integral, IY,Z=0π/2(tan(x))Y(cos(x))Z2cos(Zx)dxI_{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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