playwithfunctions4

Calculus Level 3

Let

\[f\left( b \right) =\displaystyle\int _{ 0 }^{ \pi }{ x\frac { dx }{ { b }^{ 2 }-{ cos }^{ 2 }x } } \] for \(b>1\), then

\[\frac { 15 }{ { \pi }^{ 2 } } f\left( \frac { 5 }{ 4 } \right) \] is equal to

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