Integration of square root of quadratic

Calculus Level pending

\[\large \int _{ \frac { \sqrt { 15 } }{ 3 } -1 }^{ \sqrt { 5 } -1 }{ \frac { \sqrt { 4{ x }^{ 2 }+8x-1 } }{ x+1 } dx } \]

If the definite integral above can be expressed in simplest form as \(\frac { a\sqrt { b } -\sqrt { c } \pi }{ d } \), find the value of \(a+b+c+d\).

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