# 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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