\[ y''(x)-\frac {1}{\left (a y(x)^2+b x y(x)+c x^2+d y(x)+e x+k\right )^{3/2}}=0 \] ✗ Mathematica : cpu = 60.3824 (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 = 25.336 (sec), leaf count = 8427
\[ \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 -{\alpha }^{2}c+\alpha \,\beta \,b-{b}^{2}\gamma \right ) }}} \right ) ca+\arctan \left ( 1/2\,{\frac {4\,acx-{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}}\!{(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 ( {\it \_C1}\,{b}^{6}-1024\,\gamma \,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}{c}^{2}-64\,\gamma \,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}-1024\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}\beta \,{c}^{2}+256\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{\alpha }^{2}{c}^{2}+768\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{b}^{2}{c}^{2}-64\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}\beta -192\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}c+16\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}a{\alpha }^{2}{b}^{4}+32\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}a\alpha \,{b}^{5}+24\,{a}^{2}{\beta }^{2}{{\it \_g}}^{2}\alpha \,b-16\,{a}^{2}c{\alpha }^{2}{{\it \_g}}^{2}\beta +8\,ac{\alpha }^{3}{{\it \_g}}^{2}b+4\,ac{\alpha }^{2}{{\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\,{a}^{3}{\beta }^{3}{{\it \_g}}^{2}+16\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}a{b}^{6}-1024\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}{c}^{3}+64\,{\gamma }^{2}c{a}^{3}{{\it \_g}}^{2}-16\,{b}^{2}{\gamma }^{2}{a}^{2}{{\it \_g}}^{2}-16\,{a}^{3}{\beta }^{2}{{\it \_g}}^{2}\gamma +64\,\gamma \,{c}^{2}{a}^{3}{{\it \_g}}^{2}+4\,{b}^{4}\gamma \,a{{\it \_g}}^{2}-64\,{\it \_C1}\,{a}^{3}{c}^{3}+{\it \_C1}\,{\alpha }^{2}{b}^{4}+2\,{\it \_C1}\,\alpha \,{b}^{5}-4\,\beta \,{b}^{3}\alpha \,a{{\it \_g}}^{2}+16\,\beta \,b\alpha \,{a}^{2}{{\it \_g}}^{2}\gamma -32\,\gamma \,c{a}^{2}{{\it \_g}}^{2}\alpha \,b+16\,\beta \,b\alpha \,{a}^{2}{{\it \_g}}^{2}c-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}+64\,\gamma \,c{a}^{3}{{\it \_g}}^{2}\beta -32\,\gamma \,c{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-16\,{b}^{2}\gamma \,{a}^{2}{{\it \_g}}^{2}\beta -32\,\gamma \,c{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,{b}^{2}\gamma \,a{{\it \_g}}^{2}{\alpha }^{2}+8\,{b}^{3}\gamma \,a{{\it \_g}}^{2}\alpha +512\,\gamma \,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{b}^{2}c+512\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}\alpha \,b{c}^{2}+512\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{b}^{2}\beta \,c-128\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{\alpha }^{2}{b}^{2}c-256\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}\alpha \,{b}^{3}c+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 }^{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}{c}^{2}{\alpha }^{2}{{\it \_g}}^{2}+4\,ac{\alpha }^{4}{{\it \_g}}^{2} \right ) }} \left ( -1024\,{a}^{4}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{c}^{2}\gamma +512\,{a}^{3}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{2}c\gamma -64\,{a}^{2}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{4}\gamma -1024\,{a}^{4}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{6}+16\,\gamma \,c{a}^{2}\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}-4\,{b}^{2}\gamma \,a\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}-4\,{a}^{2}{\beta }^{2}\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}-4\,ac{\alpha }^{2}\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}+4\,\beta \,b\alpha \,a\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}-16\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{\it \_C1}\,{a}^{2}{c}^{2}+8\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{\it \_C1}\,a{b}^{2}c-\sqrt {4\,a\beta +4\,ca+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 ) a\sqrt {4\,ac{x}^{2}-{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 -{\alpha }^{2}c+\alpha \,\beta \,b-{b}^{2}\gamma \right ) }}} \right ) ca+\arctan \left ( 1/2\,{\frac {4\,acx-{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}}\!{(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 ( {\it \_C1}\,{b}^{6}-1024\,\gamma \,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}{c}^{2}-64\,\gamma \,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}-1024\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}\beta \,{c}^{2}+256\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{\alpha }^{2}{c}^{2}+768\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{b}^{2}{c}^{2}-64\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}\beta -192\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{b}^{4}c+16\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}a{\alpha }^{2}{b}^{4}+32\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}a\alpha \,{b}^{5}+24\,{a}^{2}{\beta }^{2}{{\it \_g}}^{2}\alpha \,b-16\,{a}^{2}c{\alpha }^{2}{{\it \_g}}^{2}\beta +8\,ac{\alpha }^{3}{{\it \_g}}^{2}b+4\,ac{\alpha }^{2}{{\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\,{a}^{3}{\beta }^{3}{{\it \_g}}^{2}+16\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}a{b}^{6}-1024\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{4}{c}^{3}+64\,{\gamma }^{2}c{a}^{3}{{\it \_g}}^{2}-16\,{b}^{2}{\gamma }^{2}{a}^{2}{{\it \_g}}^{2}-16\,{a}^{3}{\beta }^{2}{{\it \_g}}^{2}\gamma +64\,\gamma \,{c}^{2}{a}^{3}{{\it \_g}}^{2}+4\,{b}^{4}\gamma \,a{{\it \_g}}^{2}-64\,{\it \_C1}\,{a}^{3}{c}^{3}+{\it \_C1}\,{\alpha }^{2}{b}^{4}+2\,{\it \_C1}\,\alpha \,{b}^{5}-4\,\beta \,{b}^{3}\alpha \,a{{\it \_g}}^{2}+16\,\beta \,b\alpha \,{a}^{2}{{\it \_g}}^{2}\gamma -32\,\gamma \,c{a}^{2}{{\it \_g}}^{2}\alpha \,b+16\,\beta \,b\alpha \,{a}^{2}{{\it \_g}}^{2}c-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}+64\,\gamma \,c{a}^{3}{{\it \_g}}^{2}\beta -32\,\gamma \,c{a}^{2}{{\it \_g}}^{2}{\alpha }^{2}-16\,{b}^{2}\gamma \,{a}^{2}{{\it \_g}}^{2}\beta -32\,\gamma \,c{a}^{2}{{\it \_g}}^{2}{b}^{2}+4\,{b}^{2}\gamma \,a{{\it \_g}}^{2}{\alpha }^{2}+8\,{b}^{3}\gamma \,a{{\it \_g}}^{2}\alpha +512\,\gamma \,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{b}^{2}c+512\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}\alpha \,b{c}^{2}+512\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{3}{b}^{2}\beta \,c-128\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}{\alpha }^{2}{b}^{2}c-256\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{a}^{2}\alpha \,{b}^{3}c+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 }^{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}{c}^{2}{\alpha }^{2}{{\it \_g}}^{2}+4\,ac{\alpha }^{4}{{\it \_g}}^{2} \right ) }} \left ( -1024\,{a}^{4}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{c}^{2}\gamma +512\,{a}^{3}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{2}c\gamma -64\,{a}^{2}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{4}\gamma -1024\,{a}^{4}\int \!1/4\,{\frac {\sqrt {16}}{ \left ( 4\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+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\,ca-{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\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2} \right ) }{a}}}}}}\,{\rm d}{\it \_g}{b}^{6}+16\,\gamma \,c{a}^{2}\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}-4\,{b}^{2}\gamma \,a\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}-4\,{a}^{2}{\beta }^{2}\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}-4\,ac{\alpha }^{2}\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}+4\,\beta \,b\alpha \,a\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{{\it \_g}}^{2}-16\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{\it \_C1}\,{a}^{2}{c}^{2}+8\,\sqrt {4\,a\beta +4\,ca+4\,a\gamma -{\alpha }^{2}-2\,\alpha \,b-{b}^{2}}{\it \_C1}\,a{b}^{2}c-\sqrt {4\,a\beta +4\,ca+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 ) a\sqrt {4\,ac{x}^{2}-{b}^{2}{x}^{2}+4\,a\beta \,x-2\,\alpha \,bx+4\,a\gamma -{\alpha }^{2}}-bx-\alpha \right ) } \right \} \]