Simple Integration

Calculus Level pending

\(I =\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { dx }{ { ({ a }^{ 2 }\cos ^{ 2 }{ x } +{ b }^{ 2 }\sin ^{ 2 }{ x } ) }^{ 2 } } }\)

If \(I =\frac { ({ a }^{ \alpha }+{ b }^{ \alpha })\pi }{ { \beta }^{ \gamma }{ a }^{ \delta }{ b }^{ \delta } }\) ,find \(\alpha +\beta +\gamma +\delta\) where \(\beta\) is prime.

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