\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( a \left ( y \left ( x \right ) \right ) ^{2}+bxy \left ( x \right ) +c{x}^{2}+\alpha \,y \left ( x \right ) +\beta \,x+\gamma \right ) ^{-{\frac {3}{2}}}=0} \]
Mathematica: cpu = 60.655702 (sec), leaf count = 42 \[ \text {DSolve}\left [y''(x)-\frac {1}{\left (a y(x)^2+b x y(x)+c x^2+d y(x)+e x+k\right )^{3/2}}=0,y(x),x\right ] \]
Maple: cpu = 59.530 (sec), leaf count = 13291 \[ \left \{ y \left ( x \right ) ={\frac {1}{2\,a} \left ( 2\,{\it RootOf} \left ( -4\,\arctan \left ( 1/2\,{\frac {4\,acx-{b}^{2}x+2\,a\beta - \alpha \,b}{\sqrt {a \left ( -a{\beta }^{2}+4\,ac\gamma -c{\alpha }^{2}+b \beta \,\alpha -\gamma \,{b}^{2} \right ) }}} \right ) ac+\arctan \left ( 1/ 2\,{\frac {4\,acx-{b}^{2}x+2\,a\beta -\alpha \,b}{\sqrt {a \left ( -a{ \beta }^{2}+4\,ac\gamma -c{\alpha }^{2}+b\beta \,\alpha -\gamma \,{b}^{2} \right ) }}} \right ) {b}^{2}-2\,\int ^{{\it \_Z}}\!{(16\,{a}^{2}{c}^{2 }-8\,a{b}^{2}c+{b}^{4})\sqrt {-{\frac {1}{16\,{a}^{2}{c}^{2}-8\,a{b}^{ 2}c+{b}^{4}} \left ( 64\,{a}^{3}{\gamma }^{2}c{{\it \_g}}^{2}-16\,{a}^{2 }{\gamma }^{2}{b}^{2}{{\it \_g}}^{2}-16\,{a}^{3}{\beta }^{2}{{\it \_g}}^ {2}\gamma +64\,{a}^{3}\gamma \,{c}^{2}{{\it \_g}}^{2}+4\,a\gamma \,{b}^{4 }{{\it \_g}}^{2}+16\,\beta \,b\alpha \,{a}^{2}{{\it \_g}}^{2}c+16\,\beta \,b\alpha \,{a}^{2}{{\it \_g}}^{2}\gamma -32\,{a}^{2}\gamma \,c{{\it \_g} }^{2}\alpha \,b+64\,{a}^{3}\gamma \,c{{\it \_g}}^{2}\beta -32\,{a}^{2} \gamma \,c{{\it \_g}}^{2}{\alpha }^{2}-16\,{a}^{2}\gamma \,{b}^{2}{{\it \_g}}^{2}\beta -32\,{a}^{2}\gamma \,c{{\it \_g}}^{2}{b}^{2}+4\,a\gamma \, {b}^{2}{{\it \_g}}^{2}{\alpha }^{2}+8\,a\gamma \,{b}^{3}{{\it \_g}}^{2} \alpha +{\it \_C1}\,{b}^{6}+4\,{a}^{2}{\beta }^{2}{{\it \_g}}^{2}{b}^{2} -16\,{\alpha }^{2}{a}^{2}{c}^{2}{{\it \_g}}^{2}+4\,{\alpha }^{4}ac{{\it \_g}}^{2}-16\,{a}^{3}{\beta }^{2}{{\it \_g}}^{2}c+4\,{a}^{2}{\beta }^{2} {{\it \_g}}^{2}{\alpha }^{2}-64\,\gamma \,{\it \_C1}\,{a}^{3}{c}^{2}-4\, \gamma \,{\it \_C1}\,a{b}^{4}-64\,{\it \_C1}\,{a}^{3}{c}^{3}+{\it \_C1} \,{\alpha }^{2}{b}^{4}+2\,{\it \_C1}\,\alpha \,{b}^{5}-64\,{\it \_C1}\,{ a}^{3}\beta \,{c}^{2}+16\,{\it \_C1}\,{a}^{2}{\alpha }^{2}{c}^{2}+48\,{ \it \_C1}\,{a}^{2}{b}^{2}{c}^{2}-4\,{\it \_C1}\,a{b}^{4}\beta -12\,{ \it \_C1}\,a{b}^{4}c-1024\,\gamma \,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{ \alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2} {a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a }^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+ 16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2} -8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4 \,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}} \,{\rm d}{\it \_g}{a}^{4}{c}^{2}-64\,\gamma \,\sqrt {4\,a\beta +4\,ac+4 \,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{{ \it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{ \it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{ \frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{ \it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^ {2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g }}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b} ^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}-1024\,\sqrt {4\,a\beta +4 \,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{\frac {1}{64 \,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\, {{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}} {\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{ {\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}} ^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b- {b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}\beta \,{c}^{2}+256\,\sqrt {4 \,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{ \frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3} {b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{ 2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta + 16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2 }{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a} ^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{\alpha }^{2}{c}^{2} +768\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^ {2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g} }^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{ 2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g }}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3} \gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2} \alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma - {\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{b} ^{2}{c}^{2}-64\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}- 32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16 \,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a }^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^ {2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{ \it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,a c+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}\beta -192\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4 }{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{ b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{ \frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16 \,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8 \,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\, a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}} \,{\rm d}{\it \_g}{a}^{2}{b}^{4}c+16\,\sqrt {4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{ \frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{ \it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^ {2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g }}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b} ^{2}}{a}}}}}}\,{\rm d}{\it \_g}a{\alpha }^{2}{b}^{4}+32\,\sqrt {4\,a \beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{ \frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3} {b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{ 2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta + 16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2 }{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a} ^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}a\alpha \,{b}^{5}+512\, \gamma \,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b }^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{ c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{ \it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^ {3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^ {2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a} ^{3}{b}^{2}c+512\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}- 32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16 \,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a }^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^ {2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{ \it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,a c+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}\alpha \,b{c}^{2}+512\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{ \alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2} {a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a }^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+ 16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2} -8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4 \,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}} \,{\rm d}{\it \_g}{a}^{3}{b}^{2}\beta \,c-128\,\sqrt {4\,a\beta +4\,ac+4 \,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{{ \it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{ \it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{ \frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{ \it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^ {2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g }}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b} ^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{\alpha }^{2}{b}^{2}c-256\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{ \frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3} {b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{ 2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta + 16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2 }{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a} ^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}\alpha \,{b}^{3}c- 1024\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^ {2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g} }^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{ 2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g }}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3} \gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2} \alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma - {\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}{c} ^{3}+16\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{ b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{ c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{ \it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^ {3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^ {2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}a{b }^{6}+32\,{\it \_C1}\,{a}^{2}\alpha \,b{c}^{2}+32\,{\it \_C1}\,{a}^{2}{ b}^{2}\beta \,c-8\,{\it \_C1}\,a{\alpha }^{2}{b}^{2}c-16\,{\it \_C1}\,a \alpha \,{b}^{3}c+32\,\gamma \,{\it \_C1}\,{a}^{2}{b}^{2}c-16\,{a}^{3}{ \beta }^{3}{{\it \_g}}^{2}-4\,\beta \,b{\alpha }^{3}a{{\it \_g}}^{2}-8\, \beta \,{b}^{2}{\alpha }^{2}a{{\it \_g}}^{2}-4\,\beta \,{b}^{3}\alpha \,a{ {\it \_g}}^{2}+24\,{a}^{2}{\beta }^{2}{{\it \_g}}^{2}\alpha \,b-16\,{ \alpha }^{2}{a}^{2}c{{\it \_g}}^{2}\beta +8\,{\alpha }^{3}ac{{\it \_g}}^{ 2}b+4\,{\alpha }^{2}ac{{\it \_g}}^{2}{b}^{2} \right ) }} \left ( -1024\, \gamma \,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{ c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{ \it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^ {3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^ {2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a} ^{4}{c}^{2}+512\,\gamma \,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{ c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b} ^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{ \it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a }^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a \beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}} \,{\rm d}{\it \_g}{a}^{3}{b}^{2}c-64\,\gamma \,\int \!{\frac {1}{64\,{{ \it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{ \it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{ \frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{ \it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^ {2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g }}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b} ^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}-1024\,\int \!{\frac {1}{ 64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4 \,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4 }}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3 }{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g }}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b- {b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}\beta \,{c}^{2}-1024\,\int \!{ \frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3} {b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{ 2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta + 16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2 }{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a} ^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}{c}^{3}+256\,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^ {3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b }^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2} \beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\, {a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b- 4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{ 2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{\alpha }^{2}{ c}^{2}+512\,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{ \it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^ {2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{ {\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a} ^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}} ^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a} ^{3}\alpha \,b{c}^{2}+512\,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4} {c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b }^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{ \frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16 \,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8 \,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\, a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}} \,{\rm d}{\it \_g}{a}^{3}{b}^{2}\beta \,c+768\,\int \!{\frac {1}{64\,{{ \it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{ \it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{ \frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{ \it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^ {2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g }}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b} ^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{b}^{2}{c}^{2}-128\,\int \!{ \frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3} {b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{ 2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta + 16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2 }{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a} ^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{\alpha }^{2}{b}^{2} c-256\,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{ c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{ \it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^ {3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^ {2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a} ^{2}\alpha \,{b}^{3}c-64\,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{ c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b} ^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{ \it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a }^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a \beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}} \,{\rm d}{\it \_g}{a}^{2}{b}^{4}\beta -192\,\int \!{\frac {1}{64\,{{ \it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{ \it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{ \frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{ \it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^ {2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g }}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b} ^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}c+16\,\int \!{\frac {1}{ 64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4 \,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4 }}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3 }{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g }}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b- {b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}a{\alpha }^{2}{b}^{4}+32\,\int \!{ \frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3} {b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{ 2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta + 16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2 }{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a} ^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}a\alpha \,{b}^{5}+16\,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^ {3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b }^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2} \beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\, {a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b- 4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{ 2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}a{b}^{6}+16\,{a}^{2} \gamma \,c\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{ b}^{2}}{{\it \_g}}^{2}-4\,a\gamma \,{b}^{2}\sqrt {4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}-4\,{a}^{2}{ \beta }^{2}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b- {b}^{2}}{{\it \_g}}^{2}-4\,{\alpha }^{2}ac\sqrt {4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}+4\,\beta \,b \alpha \,a\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{ b}^{2}}{{\it \_g}}^{2}-16\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^ {2}-2\,\alpha \,b-{b}^{2}}{\it \_C1}\,{a}^{2}{c}^{2}+8\,\sqrt {4\,a \beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{\it \_C1}\,a {b}^{2}c-\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{ b}^{2}}{\it \_C1}\,{b}^{4} \right ) ^{-1}}{d{\it \_g}}\sqrt {a \left ( - a{\beta }^{2}+4\,ac\gamma -c{\alpha }^{2}+b\beta \,\alpha -\gamma \,{b}^{2} \right ) }+2\,{\it \_C2}\,\sqrt {a \left ( -a{\beta }^{2}+4\,ac\gamma -c{ \alpha }^{2}+b\beta \,\alpha -\gamma \,{b}^{2} \right ) } \right ) a\sqrt {4 \,a{x}^{2}c-{b}^{2}{x}^{2}+4\,a\beta \,x-2\,\alpha \,bx+4\,a\gamma -{ \alpha }^{2}}-bx-\alpha \right ) },y \left ( x \right ) ={\frac {1}{2\,a} \left ( 2\,{\it RootOf} \left ( -4\,\arctan \left ( 1/2\,{\frac {4\,acx- {b}^{2}x+2\,a\beta -\alpha \,b}{\sqrt {a \left ( -a{\beta }^{2}+4\,ac \gamma -c{\alpha }^{2}+b\beta \,\alpha -\gamma \,{b}^{2} \right ) }}} \right ) ac+\arctan \left ( 1/2\,{\frac {4\,acx-{b}^{2}x+2\,a\beta - \alpha \,b}{\sqrt {a \left ( -a{\beta }^{2}+4\,ac\gamma -c{\alpha }^{2}+b \beta \,\alpha -\gamma \,{b}^{2} \right ) }}} \right ) {b}^{2}+2\,\int ^{{ \it \_Z}}\!{(16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4})\sqrt {-{\frac {1 }{16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}} \left ( 64\,{a}^{3}{\gamma }^ {2}c{{\it \_g}}^{2}-16\,{a}^{2}{\gamma }^{2}{b}^{2}{{\it \_g}}^{2}-16\, {a}^{3}{\beta }^{2}{{\it \_g}}^{2}\gamma +64\,{a}^{3}\gamma \,{c}^{2}{{ \it \_g}}^{2}+4\,a\gamma \,{b}^{4}{{\it \_g}}^{2}+16\,\beta \,b\alpha \,{ a}^{2}{{\it \_g}}^{2}c+16\,\beta \,b\alpha \,{a}^{2}{{\it \_g}}^{2} \gamma -32\,{a}^{2}\gamma \,c{{\it \_g}}^{2}\alpha \,b+64\,{a}^{3}\gamma \,c{{\it \_g}}^{2}\beta -32\,{a}^{2}\gamma \,c{{\it \_g}}^{2}{\alpha }^{2 }-16\,{a}^{2}\gamma \,{b}^{2}{{\it \_g}}^{2}\beta -32\,{a}^{2}\gamma \,c{ {\it \_g}}^{2}{b}^{2}+4\,a\gamma \,{b}^{2}{{\it \_g}}^{2}{\alpha }^{2}+8 \,a\gamma \,{b}^{3}{{\it \_g}}^{2}\alpha +{\it \_C1}\,{b}^{6}+4\,{a}^{2} {\beta }^{2}{{\it \_g}}^{2}{b}^{2}-16\,{\alpha }^{2}{a}^{2}{c}^{2}{{\it \_g}}^{2}+4\,{\alpha }^{4}ac{{\it \_g}}^{2}-16\,{a}^{3}{\beta }^{2}{{ \it \_g}}^{2}c+4\,{a}^{2}{\beta }^{2}{{\it \_g}}^{2}{\alpha }^{2}-64\, \gamma \,{\it \_C1}\,{a}^{3}{c}^{2}-4\,\gamma \,{\it \_C1}\,a{b}^{4}-64 \,{\it \_C1}\,{a}^{3}{c}^{3}+{\it \_C1}\,{\alpha }^{2}{b}^{4}+2\,{\it \_C1}\,\alpha \,{b}^{5}-64\,{\it \_C1}\,{a}^{3}\beta \,{c}^{2}+16\,{\it \_C1}\,{a}^{2}{\alpha }^{2}{c}^{2}+48\,{\it \_C1}\,{a}^{2}{b}^{2}{c}^{2 }-4\,{\it \_C1}\,a{b}^{4}\beta -12\,{\it \_C1}\,a{b}^{4}c-1024\,\gamma \,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}} \int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2 }{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8 \,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{ 2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4 \,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \, b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha } ^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}{c}^{2}-64 \,\gamma \,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b- {b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{ c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{ \it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^ {3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^ {2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a} ^{2}{b}^{4}-1024\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}- 32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16 \,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a }^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^ {2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{ \it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,a c+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}\beta \,{c}^{2}+256\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{ \alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2} {a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a }^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+ 16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2} -8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4 \,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}} \,{\rm d}{\it \_g}{a}^{3}{\alpha }^{2}{c}^{2}+768\,\sqrt {4\,a\beta +4\, ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{\frac {1}{64\, {{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{ \it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{ \frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{ \it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^ {2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g }}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b} ^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{b}^{2}{c}^{2}-64\,\sqrt {4\,a \beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{ \frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3} {b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{ 2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta + 16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2 }{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a} ^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}\beta -192\, \sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}} \int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2 }{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8 \,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{ 2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4 \,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \, b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha } ^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}c+16 \,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}} \int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2 }{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8 \,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{ 2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4 \,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \, b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha } ^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}a{\alpha }^{2}{b}^{ 4}+32\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b} ^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g }}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^ {2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3} \gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2} \alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma - {\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}a\alpha \,{ b}^{5}+512\,\gamma \,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}- 32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16 \,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a }^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^ {2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{ \it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,a c+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{b}^{2}c+512\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2 }-2\,\alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c} ^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{ 4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac { 16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2 }{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4 \,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{ \it \_g}{a}^{3}\alpha \,b{c}^{2}+512\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{ 2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2} {a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{ \sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^ {2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^ {2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}} }}}\,{\rm d}{\it \_g}{a}^{3}{b}^{2}\beta \,c-128\,\sqrt {4\,a\beta +4\,a c+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{\frac {1}{64\,{ {\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{ \it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{ \frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{ \it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^ {2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g }}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b} ^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{\alpha }^{2}{b}^{2}c-256\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!{ \frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3} {b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{ 2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta + 16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2 }{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a} ^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}\alpha \,{b}^{3}c- 1024\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^ {2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g} }^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{ 2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g }}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3} \gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2} \alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma - {\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}{c} ^{3}+16\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{ b}^{2}}\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{ c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{ \it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^ {3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^ {2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}a{b }^{6}+32\,{\it \_C1}\,{a}^{2}\alpha \,b{c}^{2}+32\,{\it \_C1}\,{a}^{2}{ b}^{2}\beta \,c-8\,{\it \_C1}\,a{\alpha }^{2}{b}^{2}c-16\,{\it \_C1}\,a \alpha \,{b}^{3}c+32\,\gamma \,{\it \_C1}\,{a}^{2}{b}^{2}c-16\,{a}^{3}{ \beta }^{3}{{\it \_g}}^{2}-4\,\beta \,b{\alpha }^{3}a{{\it \_g}}^{2}-8\, \beta \,{b}^{2}{\alpha }^{2}a{{\it \_g}}^{2}-4\,\beta \,{b}^{3}\alpha \,a{ {\it \_g}}^{2}+24\,{a}^{2}{\beta }^{2}{{\it \_g}}^{2}\alpha \,b-16\,{ \alpha }^{2}{a}^{2}c{{\it \_g}}^{2}\beta +8\,{\alpha }^{3}ac{{\it \_g}}^{ 2}b+4\,{\alpha }^{2}ac{{\it \_g}}^{2}{b}^{2} \right ) }} \left ( -1024\, \gamma \,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{ c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{ \it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^ {3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^ {2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a} ^{4}{c}^{2}+512\,\gamma \,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{ c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b} ^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{ \it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a }^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a \beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}} \,{\rm d}{\it \_g}{a}^{3}{b}^{2}c-64\,\gamma \,\int \!{\frac {1}{64\,{{ \it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{ \it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{ \frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{ \it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^ {2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g }}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b} ^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}-1024\,\int \!{\frac {1}{ 64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4 \,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4 }}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3 }{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g }}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b- {b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}\beta \,{c}^{2}-1024\,\int \!{ \frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3} {b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{ 2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta + 16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2 }{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a} ^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}{c}^{3}+256\,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^ {3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b }^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2} \beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\, {a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b- 4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{ 2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{\alpha }^{2}{ c}^{2}+512\,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{ \it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^ {2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{ {\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a} ^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}} ^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a} ^{3}\alpha \,b{c}^{2}+512\,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4} {c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b }^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{ \frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16 \,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8 \,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\, a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}} \,{\rm d}{\it \_g}{a}^{3}{b}^{2}\beta \,c+768\,\int \!{\frac {1}{64\,{{ \it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{ \it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{ \frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{ \it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^ {2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g }}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b} ^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{b}^{2}{c}^{2}-128\,\int \!{ \frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3} {b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{ 2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta + 16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2 }{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a} ^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{\alpha }^{2}{b}^{2} c-256\,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{ c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{ \it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^ {3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^ {2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a} ^{2}\alpha \,{b}^{3}c-64\,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{ c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b} ^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{ \it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a }^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a \beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}}}}}} \,{\rm d}{\it \_g}{a}^{2}{b}^{4}\beta -192\,\int \!{\frac {1}{64\,{{ \it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4\,{{ \it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}}{ \frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3}{{ \it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g}}^ {2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g }}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b} ^{2}}{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}c+16\,\int \!{\frac {1}{ 64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3}{b}^{2}c+4 \,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4 }}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta +16\,{a}^{3 }{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2}{{\it \_g }}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b- {b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}a{\alpha }^{2}{b}^{4}+32\,\int \!{ \frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^{3} {b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b}^{ 2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2}\beta + 16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\,{a}^{2 }{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b-4\,{a} ^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\, \alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}a\alpha \,{b}^{5}+16\,\int \!{\frac {1}{64\,{{\it \_g}}^{2}{a}^{4}{c}^{2}-32\,{{\it \_g}}^{2}{a}^ {3}{b}^{2}c+4\,{{\it \_g}}^{2}{a}^{2}{b}^{4}+16\,{a}^{2}{c}^{2}-8\,a{b }^{2}c+{b}^{4}}{\frac {1}{\sqrt {{\frac {16\,{a}^{3}{{\it \_g}}^{2} \beta +16\,{a}^{3}{{\it \_g}}^{2}c+16\,{{\it \_g}}^{2}{a}^{3}\gamma -4\, {a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-8\,{a}^{2}{{\it \_g}}^{2}\alpha \,b- 4\,{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{ 2}-2\,\alpha \,b-{b}^{2}}{a}}}}}}\,{\rm d}{\it \_g}a{b}^{6}+16\,{a}^{2} \gamma \,c\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{ b}^{2}}{{\it \_g}}^{2}-4\,a\gamma \,{b}^{2}\sqrt {4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}-4\,{a}^{2}{ \beta }^{2}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b- {b}^{2}}{{\it \_g}}^{2}-4\,{\alpha }^{2}ac\sqrt {4\,a\beta +4\,ac+4\,a \gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}+4\,\beta \,b \alpha \,a\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{ b}^{2}}{{\it \_g}}^{2}-16\,\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^ {2}-2\,\alpha \,b-{b}^{2}}{\it \_C1}\,{a}^{2}{c}^{2}+8\,\sqrt {4\,a \beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{\it \_C1}\,a {b}^{2}c-\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{ b}^{2}}{\it \_C1}\,{b}^{4} \right ) ^{-1}}{d{\it \_g}}\sqrt {a \left ( - a{\beta }^{2}+4\,ac\gamma -c{\alpha }^{2}+b\beta \,\alpha -\gamma \,{b}^{2} \right ) }+2\,{\it \_C2}\,\sqrt {a \left ( -a{\beta }^{2}+4\,ac\gamma -c{ \alpha }^{2}+b\beta \,\alpha -\gamma \,{b}^{2} \right ) } \right ) a\sqrt {4 \,a{x}^{2}c-{b}^{2}{x}^{2}+4\,a\beta \,x-2\,\alpha \,bx+4\,a\gamma -{ \alpha }^{2}}-bx-\alpha \right ) } \right \} \]