\[ y''(x)-\frac {1}{\left (a y(x)^2+b x y(x)+c x^2+d y(x)+e x+k\right )^{3/2}}=0 \] ✗ Mathematica : cpu = 60.71 (sec), leaf count = 0 , could not solve
DSolve[-(k + e*x + c*x^2 + d*y[x] + b*x*y[x] + a*y[x]^2)^(-3/2) + Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 32.429 (sec), leaf count = 8411
\[ \left \{ y \left ( x \right ) ={\frac {1}{2\,a} \left ( 2\,{\it RootOf} \left ( -4\,\arctan \left ( 1/2\,{\frac {4\,cxa-{b}^{2}x+2\,a\beta -\alpha \,b}{\sqrt {a \left ( -a{\beta }^{2}+4\,ac\gamma -{\alpha }^{2}c+\alpha \,\beta \,b-{b}^{2}\gamma \right ) }}} \right ) ac+\arctan \left ( 1/2\,{\frac {4\,cxa-{b}^{2}x+2\,a\beta -\alpha \,b}{\sqrt {a \left ( -a{\beta }^{2}+4\,ac\gamma -{\alpha }^{2}c+\alpha \,\beta \,b-{b}^{2}\gamma \right ) }}} \right ) {b}^{2}-2\,\int ^{{\it \_Z}}\!{ \left ( 4\,ac-{b}^{2} \right ) ^{2}\sqrt {-{\frac {1}{16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}} \left ( 16\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}a{\alpha }^{2}{b}^{4}+32\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}a\alpha \,{b}^{5}-1024\,\gamma \,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{4}{c}^{2}-64\,\gamma \,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{2}{b}^{4}-1024\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{4}\beta \,{c}^{2}+256\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{3}{\alpha }^{2}{c}^{2}+768\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{3}{b}^{2}{c}^{2}-64\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{2}{b}^{4}\beta -192\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{2}{b}^{4}c-128\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{2}{\alpha }^{2}{b}^{2}c-256\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{2}\alpha \,{b}^{3}c+512\,\gamma \,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{3}{b}^{2}c+512\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{3}\alpha \,b{c}^{2}+512\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{3}{b}^{2}\beta \,c+64\,{a}^{3}\gamma \,c{{\it \_g}}^{2}\beta -32\,{a}^{2}\gamma \,c{{\it \_g}}^{2}{\alpha }^{2}-16\,{a}^{2}{b}^{2}\gamma \,{{\it \_g}}^{2}\beta -32\,{a}^{2}\gamma \,c{{\it \_g}}^{2}{b}^{2}+4\,a{b}^{2}\gamma \,{{\it \_g}}^{2}{\alpha }^{2}+8\,a{b}^{3}\gamma \,{{\it \_g}}^{2}\alpha +16\,\beta \,b\alpha \,{a}^{2}{{\it \_g}}^{2}c-4\,\beta \,{b}^{3}\alpha \,a{{\it \_g}}^{2}+24\,{a}^{2}{\beta }^{2}{{\it \_g}}^{2}\alpha \,b-16\,{a}^{2}{\alpha }^{2}c{{\it \_g}}^{2}\beta +8\,a{\alpha }^{3}c{{\it \_g}}^{2}b+4\,a{\alpha }^{2}c{{\it \_g}}^{2}{b}^{2}-4\,\beta \,b{\alpha }^{3}a{{\it \_g}}^{2}-8\,\beta \,{b}^{2}{\alpha }^{2}a{{\it \_g}}^{2}+16\,\beta \,b\alpha \,{a}^{2}{{\it \_g}}^{2}\gamma -32\,{a}^{2}\gamma \,c{{\it \_g}}^{2}\alpha \,b-16\,{a}^{3}{\beta }^{2}{{\it \_g}}^{2}c+4\,{a}^{2}{\beta }^{2}{{\it \_g}}^{2}{\alpha }^{2}+4\,{a}^{2}{\beta }^{2}{{\it \_g}}^{2}{b}^{2}-16\,{a}^{2}{\alpha }^{2}{c}^{2}{{\it \_g}}^{2}+4\,a{\alpha }^{4}c{{\it \_g}}^{2}+{\it \_C1}\,{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-64\,{\it \_C1}\,{a}^{3}{c}^{3}+{\it \_C1}\,{\alpha }^{2}{b}^{4}+2\,{\it \_C1}\,\alpha \,{b}^{5}-1024\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{4}{c}^{3}+16\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}a{b}^{6}-16\,{a}^{3}{\beta }^{3}{{\it \_g}}^{2}+64\,{a}^{3}{\gamma }^{2}c{{\it \_g}}^{2}-16\,{a}^{2}{b}^{2}{\gamma }^{2}{{\it \_g}}^{2}-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-64\,\gamma \,{\it \_C1}\,{a}^{3}{c}^{2}-4\,\gamma \,{\it \_C1}\,a{b}^{4}-16\,{a}^{3}{\beta }^{2}{{\it \_g}}^{2}\gamma +64\,{a}^{3}\gamma \,{c}^{2}{{\it \_g}}^{2}+4\,a{b}^{4}\gamma \,{{\it \_g}}^{2} \right ) }} \left ( 1024\,{a}^{4}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\gamma \,{c}^{2}-512\,{a}^{3}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\gamma \,{b}^{2}c+64\,{a}^{2}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\gamma \,{b}^{4}+1024\,{a}^{4}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\beta \,{c}^{2}+1024\,{a}^{4}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{c}^{3}-256\,{a}^{3}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{\alpha }^{2}{c}^{2}-512\,{a}^{3}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\alpha \,b{c}^{2}-512\,{a}^{3}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{2}\beta \,c-768\,{a}^{3}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{2}{c}^{2}+128\,{a}^{2}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{\alpha }^{2}{b}^{2}c+256\,{a}^{2}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\alpha \,{b}^{3}c+64\,{a}^{2}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{4}\beta +192\,{a}^{2}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{4}c-16\,a\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{\alpha }^{2}{b}^{4}-32\,a\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\alpha \,{b}^{5}-16\,a\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{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{b}^{2}\gamma \,\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\,a{\alpha }^{2}c\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 -{\alpha }^{2}c+\alpha \,\beta \,b-{b}^{2}\gamma \right ) }+2\,{\it \_C2}\,\sqrt {a \left ( -a{\beta }^{2}+4\,ac\gamma -{\alpha }^{2}c+\alpha \,\beta \,b-{b}^{2}\gamma \right ) } \right ) \sqrt {4\,ac{x}^{2}-{b}^{2}{x}^{2}+4\,a\beta \,x-2\,\alpha \,bx+4\,a\gamma -{\alpha }^{2}}a-bx-\alpha \right ) },y \left ( x \right ) ={\frac {1}{2\,a} \left ( 2\,{\it RootOf} \left ( -4\,\arctan \left ( 1/2\,{\frac {4\,cxa-{b}^{2}x+2\,a\beta -\alpha \,b}{\sqrt {a \left ( -a{\beta }^{2}+4\,ac\gamma -{\alpha }^{2}c+\alpha \,\beta \,b-{b}^{2}\gamma \right ) }}} \right ) ac+\arctan \left ( 1/2\,{\frac {4\,cxa-{b}^{2}x+2\,a\beta -\alpha \,b}{\sqrt {a \left ( -a{\beta }^{2}+4\,ac\gamma -{\alpha }^{2}c+\alpha \,\beta \,b-{b}^{2}\gamma \right ) }}} \right ) {b}^{2}+2\,\int ^{{\it \_Z}}\!{ \left ( 4\,ac-{b}^{2} \right ) ^{2}\sqrt {-{\frac {1}{16\,{a}^{2}{c}^{2}-8\,a{b}^{2}c+{b}^{4}} \left ( 16\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}a{\alpha }^{2}{b}^{4}+32\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}a\alpha \,{b}^{5}-1024\,\gamma \,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{4}{c}^{2}-64\,\gamma \,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{2}{b}^{4}-1024\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{4}\beta \,{c}^{2}+256\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{3}{\alpha }^{2}{c}^{2}+768\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{3}{b}^{2}{c}^{2}-64\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{2}{b}^{4}\beta -192\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{2}{b}^{4}c-128\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{2}{\alpha }^{2}{b}^{2}c-256\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{2}\alpha \,{b}^{3}c+512\,\gamma \,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{3}{b}^{2}c+512\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{3}\alpha \,b{c}^{2}+512\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{3}{b}^{2}\beta \,c+64\,{a}^{3}\gamma \,c{{\it \_g}}^{2}\beta -32\,{a}^{2}\gamma \,c{{\it \_g}}^{2}{\alpha }^{2}-16\,{a}^{2}{b}^{2}\gamma \,{{\it \_g}}^{2}\beta -32\,{a}^{2}\gamma \,c{{\it \_g}}^{2}{b}^{2}+4\,a{b}^{2}\gamma \,{{\it \_g}}^{2}{\alpha }^{2}+8\,a{b}^{3}\gamma \,{{\it \_g}}^{2}\alpha +16\,\beta \,b\alpha \,{a}^{2}{{\it \_g}}^{2}c-4\,\beta \,{b}^{3}\alpha \,a{{\it \_g}}^{2}+24\,{a}^{2}{\beta }^{2}{{\it \_g}}^{2}\alpha \,b-16\,{a}^{2}{\alpha }^{2}c{{\it \_g}}^{2}\beta +8\,a{\alpha }^{3}c{{\it \_g}}^{2}b+4\,a{\alpha }^{2}c{{\it \_g}}^{2}{b}^{2}-4\,\beta \,b{\alpha }^{3}a{{\it \_g}}^{2}-8\,\beta \,{b}^{2}{\alpha }^{2}a{{\it \_g}}^{2}+16\,\beta \,b\alpha \,{a}^{2}{{\it \_g}}^{2}\gamma -32\,{a}^{2}\gamma \,c{{\it \_g}}^{2}\alpha \,b-16\,{a}^{3}{\beta }^{2}{{\it \_g}}^{2}c+4\,{a}^{2}{\beta }^{2}{{\it \_g}}^{2}{\alpha }^{2}+4\,{a}^{2}{\beta }^{2}{{\it \_g}}^{2}{b}^{2}-16\,{a}^{2}{\alpha }^{2}{c}^{2}{{\it \_g}}^{2}+4\,a{\alpha }^{4}c{{\it \_g}}^{2}+{\it \_C1}\,{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-64\,{\it \_C1}\,{a}^{3}{c}^{3}+{\it \_C1}\,{\alpha }^{2}{b}^{4}+2\,{\it \_C1}\,\alpha \,{b}^{5}-1024\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{a}^{4}{c}^{3}+16\,\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\sqrt {4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}a{b}^{6}-16\,{a}^{3}{\beta }^{3}{{\it \_g}}^{2}+64\,{a}^{3}{\gamma }^{2}c{{\it \_g}}^{2}-16\,{a}^{2}{b}^{2}{\gamma }^{2}{{\it \_g}}^{2}-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-64\,\gamma \,{\it \_C1}\,{a}^{3}{c}^{2}-4\,\gamma \,{\it \_C1}\,a{b}^{4}-16\,{a}^{3}{\beta }^{2}{{\it \_g}}^{2}\gamma +64\,{a}^{3}\gamma \,{c}^{2}{{\it \_g}}^{2}+4\,a{b}^{4}\gamma \,{{\it \_g}}^{2} \right ) }} \left ( 1024\,{a}^{4}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\gamma \,{c}^{2}-512\,{a}^{3}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\gamma \,{b}^{2}c+64\,{a}^{2}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\gamma \,{b}^{4}+1024\,{a}^{4}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\beta \,{c}^{2}+1024\,{a}^{4}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{c}^{3}-256\,{a}^{3}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{\alpha }^{2}{c}^{2}-512\,{a}^{3}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\alpha \,b{c}^{2}-512\,{a}^{3}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{2}\beta \,c-768\,{a}^{3}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{2}{c}^{2}+128\,{a}^{2}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{\alpha }^{2}{b}^{2}c+256\,{a}^{2}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\alpha \,{b}^{3}c+64\,{a}^{2}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{4}\beta +192\,{a}^{2}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{4}c-16\,a\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{\alpha }^{2}{b}^{4}-32\,a\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}\alpha \,{b}^{5}-16\,a\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ac-{b}^{2} \right ) ^{2} \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) }{\frac {1}{\sqrt {{\frac { \left ( 4\,{a}^{2}{{\it \_g}}^{2}+1 \right ) \left ( 4\,a\beta +4\,ac+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{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{b}^{2}\gamma \,\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\,a{\alpha }^{2}c\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 -{\alpha }^{2}c+\alpha \,\beta \,b-{b}^{2}\gamma \right ) }+2\,{\it \_C2}\,\sqrt {a \left ( -a{\beta }^{2}+4\,ac\gamma -{\alpha }^{2}c+\alpha \,\beta \,b-{b}^{2}\gamma \right ) } \right ) \sqrt {4\,ac{x}^{2}-{b}^{2}{x}^{2}+4\,a\beta \,x-2\,\alpha \,bx+4\,a\gamma -{\alpha }^{2}}a-bx-\alpha \right ) } \right \} \]