\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) -f \left ( x \right ) \right ) \left ( y \left ( x \right ) -g \left ( x \right ) \right ) \left ( y \left ( x \right ) -{\frac {af \left ( x \right ) +bg \left ( x \right ) }{a+b}} \right ) h \left ( x \right ) -{\frac { \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) \left ( y \left ( x \right ) -g \left ( x \right ) \right ) }{f \left ( x \right ) -g \left ( x \right ) }}-{\frac { \left ( {\frac {\rm d}{{\rm d}x}}g \left ( x \right ) \right ) \left ( y \left ( x \right ) -f \left ( x \right ) \right ) }{g \left ( x \right ) -f \left ( x \right ) }}=0} \]
Mathematica: cpu = 0.753096 (sec), leaf count = 354 \[ \text {Solve}\left [-\frac {1}{3} (a-b)^{2/3} (2 a+b)^{2/3} (a+2 b)^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (a-b)^{2/3} (2 a+b)^{2/3} (a+2 b)^{2/3}-3 \text {$\#$1} a^2-3 \text {$\#$1} a b-3 \text {$\#$1} b^2+(a-b)^{2/3} (2 a+b)^{2/3} (a+2 b)^{2/3}\& ,\frac {\log \left (\frac {\frac {-2 a f(x) h(x)-a g(x) h(x)-b f(x) h(x)-2 b g(x) h(x)}{a+b}+3 h(x) y(x)}{\sqrt [3]{\frac {(f(x)-g(x))^3 \left (2 a^3 h(x)^3+3 a^2 b h(x)^3-3 a b^2 h(x)^3-2 b^3 h(x)^3\right )}{(a+b)^3}}}-\text {$\#$1}\right )}{-\text {$\#$1}^2 (a-b)^{2/3} (2 a+b)^{2/3} (a+2 b)^{2/3}+a^2+a b+b^2}\& \right ]=\int _1^x \frac {\left (\frac {(f(K[1])-g(K[1]))^3 \left (2 a^3 h(K[1])^3+3 a^2 b h(K[1])^3-3 a b^2 h(K[1])^3-2 b^3 h(K[1])^3\right )}{(a+b)^3}\right )^{2/3}}{9 h(K[1])} \, dK[1]+c_1,y(x)\right ] \]
Maple: cpu = 0.156 (sec), leaf count = 2348 \[ \left \{ y \left ( x \right ) =-{\frac {1}{9\,{a}^{3}+18\,{a}^{2}b+18\,a {b}^{2}+9\,{b}^{3}} \left ( 2\,g \left ( x \right ) {\it RootOf} \left ( - 27\,\int ^{{\it \_Z}}\!{\frac { \left ( {a}^{2}+ab+{b}^{2} \right ) ^{3} }{4\,{{\it \_a}}^{3}{a}^{6}+12\,{{\it \_a}}^{3}{a}^{5}b-3\,{{\it \_a}} ^{3}{a}^{4}{b}^{2}-26\,{{\it \_a}}^{3}{a}^{3}{b}^{3}-3\,{{\it \_a}}^{3 }{a}^{2}{b}^{4}+12\,{{\it \_a}}^{3}a{b}^{5}+4\,{{\it \_a}}^{3}{b}^{6}- 27\,{\it \_a}\,{a}^{6}-81\,{\it \_a}\,{a}^{5}b-162\,{\it \_a}\,{a}^{4} {b}^{2}-189\,{\it \_a}\,{a}^{3}{b}^{3}-162\,{\it \_a}\,{a}^{2}{b}^{4}- 81\,{\it \_a}\,a{b}^{5}-27\,{\it \_a}\,{b}^{6}+27\,{a}^{6}+81\,{a}^{5} b+162\,{a}^{4}{b}^{2}+189\,{a}^{3}{b}^{3}+162\,{a}^{2}{b}^{4}+81\,a{b} ^{5}+27\,{b}^{6}}}{d{\it \_a}}+\int \!1/3\,{\frac { \left ( \left ( g \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( g \left ( x \right ) \right ) ^{2}ab+ \left ( g \left ( x \right ) \right ) ^{2}{b}^{2}-2\,g \left ( x \right ) f \left ( x \right ) {a}^{2}-2\,g \left ( x \right ) f \left ( x \right ) ab-2\,g \left ( x \right ) f \left ( x \right ) {b}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}ab+{b}^{2} \left ( f \left ( x \right ) \right ) ^{ 2} \right ) h \left ( x \right ) }{ \left ( a+b \right ) ^{2}}}\,{\rm d}x+{ \it \_C1} \right ) {a}^{3}+3\,g \left ( x \right ) {\it RootOf} \left ( - 27\,\int ^{{\it \_Z}}\!{\frac { \left ( {a}^{2}+ab+{b}^{2} \right ) ^{3} }{4\,{{\it \_a}}^{3}{a}^{6}+12\,{{\it \_a}}^{3}{a}^{5}b-3\,{{\it \_a}} ^{3}{a}^{4}{b}^{2}-26\,{{\it \_a}}^{3}{a}^{3}{b}^{3}-3\,{{\it \_a}}^{3 }{a}^{2}{b}^{4}+12\,{{\it \_a}}^{3}a{b}^{5}+4\,{{\it \_a}}^{3}{b}^{6}- 27\,{\it \_a}\,{a}^{6}-81\,{\it \_a}\,{a}^{5}b-162\,{\it \_a}\,{a}^{4} {b}^{2}-189\,{\it \_a}\,{a}^{3}{b}^{3}-162\,{\it \_a}\,{a}^{2}{b}^{4}- 81\,{\it \_a}\,a{b}^{5}-27\,{\it \_a}\,{b}^{6}+27\,{a}^{6}+81\,{a}^{5} b+162\,{a}^{4}{b}^{2}+189\,{a}^{3}{b}^{3}+162\,{a}^{2}{b}^{4}+81\,a{b} ^{5}+27\,{b}^{6}}}{d{\it \_a}}+\int \!1/3\,{\frac { \left ( \left ( g \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( g \left ( x \right ) \right ) ^{2}ab+ \left ( g \left ( x \right ) \right ) ^{2}{b}^{2}-2\,g \left ( x \right ) f \left ( x \right ) {a}^{2}-2\,g \left ( x \right ) f \left ( x \right ) ab-2\,g \left ( x \right ) f \left ( x \right ) {b}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}ab+{b}^{2} \left ( f \left ( x \right ) \right ) ^{ 2} \right ) h \left ( x \right ) }{ \left ( a+b \right ) ^{2}}}\,{\rm d}x+{ \it \_C1} \right ) {a}^{2}b-3\,g \left ( x \right ) {\it RootOf} \left ( - 27\,\int ^{{\it \_Z}}\!{\frac { \left ( {a}^{2}+ab+{b}^{2} \right ) ^{3} }{4\,{{\it \_a}}^{3}{a}^{6}+12\,{{\it \_a}}^{3}{a}^{5}b-3\,{{\it \_a}} ^{3}{a}^{4}{b}^{2}-26\,{{\it \_a}}^{3}{a}^{3}{b}^{3}-3\,{{\it \_a}}^{3 }{a}^{2}{b}^{4}+12\,{{\it \_a}}^{3}a{b}^{5}+4\,{{\it \_a}}^{3}{b}^{6}- 27\,{\it \_a}\,{a}^{6}-81\,{\it \_a}\,{a}^{5}b-162\,{\it \_a}\,{a}^{4} {b}^{2}-189\,{\it \_a}\,{a}^{3}{b}^{3}-162\,{\it \_a}\,{a}^{2}{b}^{4}- 81\,{\it \_a}\,a{b}^{5}-27\,{\it \_a}\,{b}^{6}+27\,{a}^{6}+81\,{a}^{5} b+162\,{a}^{4}{b}^{2}+189\,{a}^{3}{b}^{3}+162\,{a}^{2}{b}^{4}+81\,a{b} ^{5}+27\,{b}^{6}}}{d{\it \_a}}+\int \!1/3\,{\frac { \left ( \left ( g \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( g \left ( x \right ) \right ) ^{2}ab+ \left ( g \left ( x \right ) \right ) ^{2}{b}^{2}-2\,g \left ( x \right ) f \left ( x \right ) {a}^{2}-2\,g \left ( x \right ) f \left ( x \right ) ab-2\,g \left ( x \right ) f \left ( x \right ) {b}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}ab+{b}^{2} \left ( f \left ( x \right ) \right ) ^{ 2} \right ) h \left ( x \right ) }{ \left ( a+b \right ) ^{2}}}\,{\rm d}x+{ \it \_C1} \right ) a{b}^{2}-2\,g \left ( x \right ) {\it RootOf} \left ( - 27\,\int ^{{\it \_Z}}\!{\frac { \left ( {a}^{2}+ab+{b}^{2} \right ) ^{3} }{4\,{{\it \_a}}^{3}{a}^{6}+12\,{{\it \_a}}^{3}{a}^{5}b-3\,{{\it \_a}} ^{3}{a}^{4}{b}^{2}-26\,{{\it \_a}}^{3}{a}^{3}{b}^{3}-3\,{{\it \_a}}^{3 }{a}^{2}{b}^{4}+12\,{{\it \_a}}^{3}a{b}^{5}+4\,{{\it \_a}}^{3}{b}^{6}- 27\,{\it \_a}\,{a}^{6}-81\,{\it \_a}\,{a}^{5}b-162\,{\it \_a}\,{a}^{4} {b}^{2}-189\,{\it \_a}\,{a}^{3}{b}^{3}-162\,{\it \_a}\,{a}^{2}{b}^{4}- 81\,{\it \_a}\,a{b}^{5}-27\,{\it \_a}\,{b}^{6}+27\,{a}^{6}+81\,{a}^{5} b+162\,{a}^{4}{b}^{2}+189\,{a}^{3}{b}^{3}+162\,{a}^{2}{b}^{4}+81\,a{b} ^{5}+27\,{b}^{6}}}{d{\it \_a}}+\int \!1/3\,{\frac { \left ( \left ( g \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( g \left ( x \right ) \right ) ^{2}ab+ \left ( g \left ( x \right ) \right ) ^{2}{b}^{2}-2\,g \left ( x \right ) f \left ( x \right ) {a}^{2}-2\,g \left ( x \right ) f \left ( x \right ) ab-2\,g \left ( x \right ) f \left ( x \right ) {b}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}ab+{b}^{2} \left ( f \left ( x \right ) \right ) ^{ 2} \right ) h \left ( x \right ) }{ \left ( a+b \right ) ^{2}}}\,{\rm d}x+{ \it \_C1} \right ) {b}^{3}-2\,f \left ( x \right ) {\it RootOf} \left ( - 27\,\int ^{{\it \_Z}}\!{\frac { \left ( {a}^{2}+ab+{b}^{2} \right ) ^{3} }{4\,{{\it \_a}}^{3}{a}^{6}+12\,{{\it \_a}}^{3}{a}^{5}b-3\,{{\it \_a}} ^{3}{a}^{4}{b}^{2}-26\,{{\it \_a}}^{3}{a}^{3}{b}^{3}-3\,{{\it \_a}}^{3 }{a}^{2}{b}^{4}+12\,{{\it \_a}}^{3}a{b}^{5}+4\,{{\it \_a}}^{3}{b}^{6}- 27\,{\it \_a}\,{a}^{6}-81\,{\it \_a}\,{a}^{5}b-162\,{\it \_a}\,{a}^{4} {b}^{2}-189\,{\it \_a}\,{a}^{3}{b}^{3}-162\,{\it \_a}\,{a}^{2}{b}^{4}- 81\,{\it \_a}\,a{b}^{5}-27\,{\it \_a}\,{b}^{6}+27\,{a}^{6}+81\,{a}^{5} b+162\,{a}^{4}{b}^{2}+189\,{a}^{3}{b}^{3}+162\,{a}^{2}{b}^{4}+81\,a{b} ^{5}+27\,{b}^{6}}}{d{\it \_a}}+\int \!1/3\,{\frac { \left ( \left ( g \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( g \left ( x \right ) \right ) ^{2}ab+ \left ( g \left ( x \right ) \right ) ^{2}{b}^{2}-2\,g \left ( x \right ) f \left ( x \right ) {a}^{2}-2\,g \left ( x \right ) f \left ( x \right ) ab-2\,g \left ( x \right ) f \left ( x \right ) {b}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}ab+{b}^{2} \left ( f \left ( x \right ) \right ) ^{ 2} \right ) h \left ( x \right ) }{ \left ( a+b \right ) ^{2}}}\,{\rm d}x+{ \it \_C1} \right ) {a}^{3}-3\,f \left ( x \right ) {\it RootOf} \left ( - 27\,\int ^{{\it \_Z}}\!{\frac { \left ( {a}^{2}+ab+{b}^{2} \right ) ^{3} }{4\,{{\it \_a}}^{3}{a}^{6}+12\,{{\it \_a}}^{3}{a}^{5}b-3\,{{\it \_a}} ^{3}{a}^{4}{b}^{2}-26\,{{\it \_a}}^{3}{a}^{3}{b}^{3}-3\,{{\it \_a}}^{3 }{a}^{2}{b}^{4}+12\,{{\it \_a}}^{3}a{b}^{5}+4\,{{\it \_a}}^{3}{b}^{6}- 27\,{\it \_a}\,{a}^{6}-81\,{\it \_a}\,{a}^{5}b-162\,{\it \_a}\,{a}^{4} {b}^{2}-189\,{\it \_a}\,{a}^{3}{b}^{3}-162\,{\it \_a}\,{a}^{2}{b}^{4}- 81\,{\it \_a}\,a{b}^{5}-27\,{\it \_a}\,{b}^{6}+27\,{a}^{6}+81\,{a}^{5} b+162\,{a}^{4}{b}^{2}+189\,{a}^{3}{b}^{3}+162\,{a}^{2}{b}^{4}+81\,a{b} ^{5}+27\,{b}^{6}}}{d{\it \_a}}+\int \!1/3\,{\frac { \left ( \left ( g \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( g \left ( x \right ) \right ) ^{2}ab+ \left ( g \left ( x \right ) \right ) ^{2}{b}^{2}-2\,g \left ( x \right ) f \left ( x \right ) {a}^{2}-2\,g \left ( x \right ) f \left ( x \right ) ab-2\,g \left ( x \right ) f \left ( x \right ) {b}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}ab+{b}^{2} \left ( f \left ( x \right ) \right ) ^{ 2} \right ) h \left ( x \right ) }{ \left ( a+b \right ) ^{2}}}\,{\rm d}x+{ \it \_C1} \right ) {a}^{2}b+3\,f \left ( x \right ) {\it RootOf} \left ( - 27\,\int ^{{\it \_Z}}\!{\frac { \left ( {a}^{2}+ab+{b}^{2} \right ) ^{3} }{4\,{{\it \_a}}^{3}{a}^{6}+12\,{{\it \_a}}^{3}{a}^{5}b-3\,{{\it \_a}} ^{3}{a}^{4}{b}^{2}-26\,{{\it \_a}}^{3}{a}^{3}{b}^{3}-3\,{{\it \_a}}^{3 }{a}^{2}{b}^{4}+12\,{{\it \_a}}^{3}a{b}^{5}+4\,{{\it \_a}}^{3}{b}^{6}- 27\,{\it \_a}\,{a}^{6}-81\,{\it \_a}\,{a}^{5}b-162\,{\it \_a}\,{a}^{4} {b}^{2}-189\,{\it \_a}\,{a}^{3}{b}^{3}-162\,{\it \_a}\,{a}^{2}{b}^{4}- 81\,{\it \_a}\,a{b}^{5}-27\,{\it \_a}\,{b}^{6}+27\,{a}^{6}+81\,{a}^{5} b+162\,{a}^{4}{b}^{2}+189\,{a}^{3}{b}^{3}+162\,{a}^{2}{b}^{4}+81\,a{b} ^{5}+27\,{b}^{6}}}{d{\it \_a}}+\int \!1/3\,{\frac { \left ( \left ( g \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( g \left ( x \right ) \right ) ^{2}ab+ \left ( g \left ( x \right ) \right ) ^{2}{b}^{2}-2\,g \left ( x \right ) f \left ( x \right ) {a}^{2}-2\,g \left ( x \right ) f \left ( x \right ) ab-2\,g \left ( x \right ) f \left ( x \right ) {b}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}ab+{b}^{2} \left ( f \left ( x \right ) \right ) ^{ 2} \right ) h \left ( x \right ) }{ \left ( a+b \right ) ^{2}}}\,{\rm d}x+{ \it \_C1} \right ) a{b}^{2}+2\,f \left ( x \right ) {\it RootOf} \left ( - 27\,\int ^{{\it \_Z}}\!{\frac { \left ( {a}^{2}+ab+{b}^{2} \right ) ^{3} }{4\,{{\it \_a}}^{3}{a}^{6}+12\,{{\it \_a}}^{3}{a}^{5}b-3\,{{\it \_a}} ^{3}{a}^{4}{b}^{2}-26\,{{\it \_a}}^{3}{a}^{3}{b}^{3}-3\,{{\it \_a}}^{3 }{a}^{2}{b}^{4}+12\,{{\it \_a}}^{3}a{b}^{5}+4\,{{\it \_a}}^{3}{b}^{6}- 27\,{\it \_a}\,{a}^{6}-81\,{\it \_a}\,{a}^{5}b-162\,{\it \_a}\,{a}^{4} {b}^{2}-189\,{\it \_a}\,{a}^{3}{b}^{3}-162\,{\it \_a}\,{a}^{2}{b}^{4}- 81\,{\it \_a}\,a{b}^{5}-27\,{\it \_a}\,{b}^{6}+27\,{a}^{6}+81\,{a}^{5} b+162\,{a}^{4}{b}^{2}+189\,{a}^{3}{b}^{3}+162\,{a}^{2}{b}^{4}+81\,a{b} ^{5}+27\,{b}^{6}}}{d{\it \_a}}+\int \!1/3\,{\frac { \left ( \left ( g \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( g \left ( x \right ) \right ) ^{2}ab+ \left ( g \left ( x \right ) \right ) ^{2}{b}^{2}-2\,g \left ( x \right ) f \left ( x \right ) {a}^{2}-2\,g \left ( x \right ) f \left ( x \right ) ab-2\,g \left ( x \right ) f \left ( x \right ) {b}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}{a}^{2}+ \left ( f \left ( x \right ) \right ) ^{2}ab+{b}^{2} \left ( f \left ( x \right ) \right ) ^{ 2} \right ) h \left ( x \right ) }{ \left ( a+b \right ) ^{2}}}\,{\rm d}x+{ \it \_C1} \right ) {b}^{3}-3\,{a}^{3}g \left ( x \right ) -9\,{a}^{2}g \left ( x \right ) b-9\,ag \left ( x \right ) {b}^{2}-6\,{b}^{3}g \left ( x \right ) -6\,{a}^{3}f \left ( x \right ) -9\,{a}^{2}f \left ( x \right ) b-9\,af \left ( x \right ) {b}^{2}-3\,{b}^{3}f \left ( x \right ) \right ) } \right \} \]
Sage: cpu = 2.588 (sec), leaf count = 0 \[ \left [\left [\frac {{\left (a^{2} + a b + b^{2}\right )} \log \left (3 \, a^{2} + 3 \, a b + 3 \, b^{2} - \frac {3 \, {\left (a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right )} {\left (a^{2} + a b - 2 \, b^{2}\right )} {\left (\frac {{\left (2 \, a + b\right )} f\left (x\right ) + {\left (a + 2 \, b\right )} g\left (x\right )}{a + b} - 3 \, y\left (x\right )\right )} {\left (\frac {{\left ({\left (a^{2} + a b + b^{2}\right )} f\left (x\right )^{3} - 3 \, {\left (a^{2} + a b + b^{2}\right )} f\left (x\right )^{2} g\left (x\right ) + 3 \, {\left (a^{2} + a b + b^{2}\right )} f\left (x\right ) g\left (x\right )^{2} - {\left (a^{2} + a b + b^{2}\right )} g\left (x\right )^{3}\right )} h\left (x\right )^{2} + 6 \, {\left (a^{2} + 2 \, a b + b^{2}\right )} h\left (x\right ) D[0]\left (f\right )\left (x\right ) - 6 \, {\left (a^{2} + 2 \, a b + b^{2}\right )} h\left (x\right ) D[0]\left (g\right )\left (x\right ) + 3 \, {\left ({\left (a^{2} + 2 \, a b + b^{2}\right )} f\left (x\right ) - {\left (a^{2} + 2 \, a b + b^{2}\right )} g\left (x\right )\right )} D[0]\left (h\right )\left (x\right )}{{\left ({\left (a^{2} + 2 \, a b + b^{2}\right )} f\left (x\right ) - {\left (a^{2} + 2 \, a b + b^{2}\right )} g\left (x\right )\right )} h\left (x\right )} - \frac {3 \, {\left (a^{6} + 6 \, a^{5} b + 15 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 6 \, a b^{5} + b^{6}\right )} {\left (\frac {2 \, {\left ({\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{5} D[0]\left (f\right )\left (x\right ) - 5 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{4} g\left (x\right ) D[0]\left (f\right )\left (x\right ) + 10 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{3} g\left (x\right )^{2} D[0]\left (f\right )\left (x\right ) - 10 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{2} g\left (x\right )^{3} D[0]\left (f\right )\left (x\right ) + 5 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right ) g\left (x\right )^{4} D[0]\left (f\right )\left (x\right ) - {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} g\left (x\right )^{5} D[0]\left (f\right )\left (x\right ) - {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{5} D[0]\left (g\right )\left (x\right ) + 5 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{4} g\left (x\right ) D[0]\left (g\right )\left (x\right ) - 10 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{3} g\left (x\right )^{2} D[0]\left (g\right )\left (x\right ) + 10 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{2} g\left (x\right )^{3} D[0]\left (g\right )\left (x\right ) - 5 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right ) g\left (x\right )^{4} D[0]\left (g\right )\left (x\right ) + {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} g\left (x\right )^{5} D[0]\left (g\right )\left (x\right )\right )} h\left (x\right )^{3}}{a^{6} + 6 \, a^{5} b + 15 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 6 \, a b^{5} + b^{6}} + \frac {{\left ({\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{6} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{5} g\left (x\right ) + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{4} g\left (x\right )^{2} - 20 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{3} g\left (x\right )^{3} + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{2} g\left (x\right )^{4} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right ) g\left (x\right )^{5} + {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} g\left (x\right )^{6}\right )} h\left (x\right )^{2} D[0]\left (h\right )\left (x\right )}{a^{6} + 6 \, a^{5} b + 15 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 6 \, a b^{5} + b^{6}}\right )}}{{\left ({\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{6} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{5} g\left (x\right ) + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{4} g\left (x\right )^{2} - 20 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{3} g\left (x\right )^{3} + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{2} g\left (x\right )^{4} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right ) g\left (x\right )^{5} + {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} g\left (x\right )^{6}\right )} h\left (x\right )^{3}}\right )}}{{\left ({\left (2 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 2 \, b^{3}\right )} f\left (x\right )^{3} - 3 \, {\left (2 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 2 \, b^{3}\right )} f\left (x\right )^{2} g\left (x\right ) + 3 \, {\left (2 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 2 \, b^{3}\right )} f\left (x\right ) g\left (x\right )^{2} - {\left (2 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 2 \, b^{3}\right )} g\left (x\right )^{3}\right )} h\left (x\right )}\right )}{3 \, {\left (a^{2} + a b\right )}} + \frac {{\left (a^{2} + a b + b^{2}\right )} \log \left (-3 \, a^{2} - 3 \, a b - 3 \, b^{2} - \frac {3 \, {\left (a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right )} {\left (2 \, a^{2} - a b - b^{2}\right )} {\left (\frac {{\left (2 \, a + b\right )} f\left (x\right ) + {\left (a + 2 \, b\right )} g\left (x\right )}{a + b} - 3 \, y\left (x\right )\right )} {\left (\frac {{\left ({\left (a^{2} + a b + b^{2}\right )} f\left (x\right )^{3} - 3 \, {\left (a^{2} + a b + b^{2}\right )} f\left (x\right )^{2} g\left (x\right ) + 3 \, {\left (a^{2} + a b + b^{2}\right )} f\left (x\right ) g\left (x\right )^{2} - {\left (a^{2} + a b + b^{2}\right )} g\left (x\right )^{3}\right )} h\left (x\right )^{2} + 6 \, {\left (a^{2} + 2 \, a b + b^{2}\right )} h\left (x\right ) D[0]\left (f\right )\left (x\right ) - 6 \, {\left (a^{2} + 2 \, a b + b^{2}\right )} h\left (x\right ) D[0]\left (g\right )\left (x\right ) + 3 \, {\left ({\left (a^{2} + 2 \, a b + b^{2}\right )} f\left (x\right ) - {\left (a^{2} + 2 \, a b + b^{2}\right )} g\left (x\right )\right )} D[0]\left (h\right )\left (x\right )}{{\left ({\left (a^{2} + 2 \, a b + b^{2}\right )} f\left (x\right ) - {\left (a^{2} + 2 \, a b + b^{2}\right )} g\left (x\right )\right )} h\left (x\right )} - \frac {3 \, {\left (a^{6} + 6 \, a^{5} b + 15 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 6 \, a b^{5} + b^{6}\right )} {\left (\frac {2 \, {\left ({\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{5} D[0]\left (f\right )\left (x\right ) - 5 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{4} g\left (x\right ) D[0]\left (f\right )\left (x\right ) + 10 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{3} g\left (x\right )^{2} D[0]\left (f\right )\left (x\right ) - 10 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{2} g\left (x\right )^{3} D[0]\left (f\right )\left (x\right ) + 5 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right ) g\left (x\right )^{4} D[0]\left (f\right )\left (x\right ) - {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} g\left (x\right )^{5} D[0]\left (f\right )\left (x\right ) - {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{5} D[0]\left (g\right )\left (x\right ) + 5 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{4} g\left (x\right ) D[0]\left (g\right )\left (x\right ) - 10 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{3} g\left (x\right )^{2} D[0]\left (g\right )\left (x\right ) + 10 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{2} g\left (x\right )^{3} D[0]\left (g\right )\left (x\right ) - 5 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right ) g\left (x\right )^{4} D[0]\left (g\right )\left (x\right ) + {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} g\left (x\right )^{5} D[0]\left (g\right )\left (x\right )\right )} h\left (x\right )^{3}}{a^{6} + 6 \, a^{5} b + 15 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 6 \, a b^{5} + b^{6}} + \frac {{\left ({\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{6} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{5} g\left (x\right ) + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{4} g\left (x\right )^{2} - 20 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{3} g\left (x\right )^{3} + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{2} g\left (x\right )^{4} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right ) g\left (x\right )^{5} + {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} g\left (x\right )^{6}\right )} h\left (x\right )^{2} D[0]\left (h\right )\left (x\right )}{a^{6} + 6 \, a^{5} b + 15 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 6 \, a b^{5} + b^{6}}\right )}}{{\left ({\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{6} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{5} g\left (x\right ) + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{4} g\left (x\right )^{2} - 20 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{3} g\left (x\right )^{3} + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{2} g\left (x\right )^{4} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right ) g\left (x\right )^{5} + {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} g\left (x\right )^{6}\right )} h\left (x\right )^{3}}\right )}}{{\left ({\left (2 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 2 \, b^{3}\right )} f\left (x\right )^{3} - 3 \, {\left (2 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 2 \, b^{3}\right )} f\left (x\right )^{2} g\left (x\right ) + 3 \, {\left (2 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 2 \, b^{3}\right )} f\left (x\right ) g\left (x\right )^{2} - {\left (2 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 2 \, b^{3}\right )} g\left (x\right )^{3}\right )} h\left (x\right )}\right )}{3 \, {\left (a b + b^{2}\right )}} - \frac {{\left (a^{2} + a b + b^{2}\right )} \log \left (3 \, a^{2} + 3 \, a b + 3 \, b^{2} + \frac {3 \, {\left (a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right )} {\left (2 \, a^{2} + 5 \, a b + 2 \, b^{2}\right )} {\left (\frac {{\left (2 \, a + b\right )} f\left (x\right ) + {\left (a + 2 \, b\right )} g\left (x\right )}{a + b} - 3 \, y\left (x\right )\right )} {\left (\frac {{\left ({\left (a^{2} + a b + b^{2}\right )} f\left (x\right )^{3} - 3 \, {\left (a^{2} + a b + b^{2}\right )} f\left (x\right )^{2} g\left (x\right ) + 3 \, {\left (a^{2} + a b + b^{2}\right )} f\left (x\right ) g\left (x\right )^{2} - {\left (a^{2} + a b + b^{2}\right )} g\left (x\right )^{3}\right )} h\left (x\right )^{2} + 6 \, {\left (a^{2} + 2 \, a b + b^{2}\right )} h\left (x\right ) D[0]\left (f\right )\left (x\right ) - 6 \, {\left (a^{2} + 2 \, a b + b^{2}\right )} h\left (x\right ) D[0]\left (g\right )\left (x\right ) + 3 \, {\left ({\left (a^{2} + 2 \, a b + b^{2}\right )} f\left (x\right ) - {\left (a^{2} + 2 \, a b + b^{2}\right )} g\left (x\right )\right )} D[0]\left (h\right )\left (x\right )}{{\left ({\left (a^{2} + 2 \, a b + b^{2}\right )} f\left (x\right ) - {\left (a^{2} + 2 \, a b + b^{2}\right )} g\left (x\right )\right )} h\left (x\right )} - \frac {3 \, {\left (a^{6} + 6 \, a^{5} b + 15 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 6 \, a b^{5} + b^{6}\right )} {\left (\frac {2 \, {\left ({\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{5} D[0]\left (f\right )\left (x\right ) - 5 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{4} g\left (x\right ) D[0]\left (f\right )\left (x\right ) + 10 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{3} g\left (x\right )^{2} D[0]\left (f\right )\left (x\right ) - 10 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{2} g\left (x\right )^{3} D[0]\left (f\right )\left (x\right ) + 5 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right ) g\left (x\right )^{4} D[0]\left (f\right )\left (x\right ) - {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} g\left (x\right )^{5} D[0]\left (f\right )\left (x\right ) - {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{5} D[0]\left (g\right )\left (x\right ) + 5 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{4} g\left (x\right ) D[0]\left (g\right )\left (x\right ) - 10 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{3} g\left (x\right )^{2} D[0]\left (g\right )\left (x\right ) + 10 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{2} g\left (x\right )^{3} D[0]\left (g\right )\left (x\right ) - 5 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right ) g\left (x\right )^{4} D[0]\left (g\right )\left (x\right ) + {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} g\left (x\right )^{5} D[0]\left (g\right )\left (x\right )\right )} h\left (x\right )^{3}}{a^{6} + 6 \, a^{5} b + 15 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 6 \, a b^{5} + b^{6}} + \frac {{\left ({\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{6} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{5} g\left (x\right ) + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{4} g\left (x\right )^{2} - 20 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{3} g\left (x\right )^{3} + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{2} g\left (x\right )^{4} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right ) g\left (x\right )^{5} + {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} g\left (x\right )^{6}\right )} h\left (x\right )^{2} D[0]\left (h\right )\left (x\right )}{a^{6} + 6 \, a^{5} b + 15 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 6 \, a b^{5} + b^{6}}\right )}}{{\left ({\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{6} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{5} g\left (x\right ) + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{4} g\left (x\right )^{2} - 20 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{3} g\left (x\right )^{3} + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{2} g\left (x\right )^{4} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right ) g\left (x\right )^{5} + {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} g\left (x\right )^{6}\right )} h\left (x\right )^{3}}\right )}}{{\left ({\left (2 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 2 \, b^{3}\right )} f\left (x\right )^{3} - 3 \, {\left (2 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 2 \, b^{3}\right )} f\left (x\right )^{2} g\left (x\right ) + 3 \, {\left (2 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 2 \, b^{3}\right )} f\left (x\right ) g\left (x\right )^{2} - {\left (2 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 2 \, b^{3}\right )} g\left (x\right )^{3}\right )} h\left (x\right )}\right )}{3 \, a b} - \int \frac {{\left ({\left (a^{2} + a b + b^{2}\right )} f\left (x\right )^{3} - 3 \, {\left (a^{2} + a b + b^{2}\right )} f\left (x\right )^{2} g\left (x\right ) + 3 \, {\left (a^{2} + a b + b^{2}\right )} f\left (x\right ) g\left (x\right )^{2} - {\left (a^{2} + a b + b^{2}\right )} g\left (x\right )^{3}\right )} h\left (x\right )^{2} + 6 \, {\left (a^{2} + 2 \, a b + b^{2}\right )} h\left (x\right ) D[0]\left (f\right )\left (x\right ) - 6 \, {\left (a^{2} + 2 \, a b + b^{2}\right )} h\left (x\right ) D[0]\left (g\right )\left (x\right ) + 3 \, {\left ({\left (a^{2} + 2 \, a b + b^{2}\right )} f\left (x\right ) - {\left (a^{2} + 2 \, a b + b^{2}\right )} g\left (x\right )\right )} D[0]\left (h\right )\left (x\right )}{3 \, {\left ({\left (a^{2} + 2 \, a b + b^{2}\right )} f\left (x\right ) - {\left (a^{2} + 2 \, a b + b^{2}\right )} g\left (x\right )\right )} h\left (x\right )}\,{d x} + \frac {1}{3} \, \log \left (-\frac {{\left ({\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{6} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{5} g\left (x\right ) + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{4} g\left (x\right )^{2} - 20 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{3} g\left (x\right )^{3} + 15 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right )^{2} g\left (x\right )^{4} - 6 \, {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} f\left (x\right ) g\left (x\right )^{5} + {\left (4 \, a^{6} + 12 \, a^{5} b - 3 \, a^{4} b^{2} - 26 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 12 \, a b^{5} + 4 \, b^{6}\right )} g\left (x\right )^{6}\right )} h\left (x\right )^{3}}{729 \, {\left (a^{6} + 6 \, a^{5} b + 15 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 6 \, a b^{5} + b^{6}\right )}}\right ) = c\right ], \text {\texttt {abel}}\right ] \]