Integrate with sin cos #3

Calculus Level 5

If \[\large{\displaystyle \int^{\frac{\pi}{2}}_{0} f(x) dx=\frac{A}{B}\pi}\]

where \(A,B\) are co prime natural numbers.

Find \(A+B\)

given that

\(\large{f\left( x \right) =5\int _{ 0 }^{ x }{ \frac { 6 }{ \sin ^{ 2 }{ \left( x \right) } } \int _{ 0 }^{ x }{ .......... } \int _{ 0 }^{ x }{ \frac { 2014 }{ \sin ^{ 2 }{ \left( x \right) } } \int _{ 0 }^{ x }{ \frac { 2015 }{ \sin ^{ 2 }{ \left( x \right) } } \int _{ 0 }^{ x }{ \frac { 2016 }{ \sin ^{ 2 }{ \left( x \right) } } } } \int _{ 0 }^{ x }{ \sin { \left( 2017x \right) \sin ^{ 2015 }{ \left( x \right) } { \left( dx \right) }^{ 2012 } } } } } }\)

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