8.31   ODE No. 1621

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+y\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-{\left(y\left(x\right)\right)}^3+ay\left(x\right)=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 100.138216 (sec), leaf count = 28 $$\text{DSolve}[ay(x)+y^{″}(x)+y(x)y^{\prime }(x)-y(x{)}^3=0,y(x),x]$$

Maple: cpu = 0.967 (sec), leaf count = 8191 $$\{{\int }^{y\left(x\right)}\frac{1}{-63{\mathit{\_}\mathit{a}}^2+63a}(\frac{{(-\frac{1}{2}-\frac{i}{2}\sqrt{3})}^3}{2}(126\frac{1}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}-126({\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3)\frac{1}{\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}}-126)+63)d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}\frac{1}{-63{\mathit{\_}\mathit{a}}^2+63a}(\frac{{(-\frac{1}{2}-\frac{i}{2}\sqrt{3})}^3}{2}(-63\frac{1}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}+63({\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3)\frac{1}{\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}}-126-4i\sqrt{3}(\frac{63}{-4{\mathit{\_}\mathit{a}}^6+12{\mathit{\_}\mathit{a}}^{4}a-12{\mathit{\_}\mathit{a}}^2{a}^2+320{\mathit{\_}\mathit{C}\mathit{1}}^3+4a^3}\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}+\frac{63{\mathit{\_}\mathit{a}}^6-189{\mathit{\_}\mathit{a}}^{4}a+189{\mathit{\_}\mathit{a}}^2{a}^2-63a^3}{4}\frac{1}{\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}}))+63)d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}\frac{1}{-63{\mathit{\_}\mathit{a}}^2+63a}(\frac{{(-\frac{1}{2}-\frac{i}{2}\sqrt{3})}^3}{2}(-63\frac{1}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}+63({\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3)\frac{1}{\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}}-126+4i\sqrt{3}(\frac{63}{-4{\mathit{\_}\mathit{a}}^6+12{\mathit{\_}\mathit{a}}^{4}a-12{\mathit{\_}\mathit{a}}^2{a}^2+320{\mathit{\_}\mathit{C}\mathit{1}}^3+4a^3}\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}+\frac{63{\mathit{\_}\mathit{a}}^6-189{\mathit{\_}\mathit{a}}^{4}a+189{\mathit{\_}\mathit{a}}^2{a}^2-63a^3}{4}\frac{1}{\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}}))+63)d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}\frac{1}{-63{\mathit{\_}\mathit{a}}^2+63a}(\frac{{(-\frac{1}{2}+\frac{i}{2}\sqrt{3})}^3}{2}(126\frac{1}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}-126({\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3)\frac{1}{\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}}-126)+63)d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int 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}^{y\left(x\right)}\frac{1}{-63{\mathit{\_}\mathit{a}}^2+63a}(-\frac{63}{-2{\mathit{\_}\mathit{a}}^6+6{\mathit{\_}\mathit{a}}^{4}a-6{\mathit{\_}\mathit{a}}^2{a}^2+160{\mathit{\_}\mathit{C}\mathit{1}}^3+2a^3}\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}+\frac{63{\mathit{\_}\mathit{a}}^6-189{\mathit{\_}\mathit{a}}^{4}a+189{\mathit{\_}\mathit{a}}^2{a}^2-63a^3}{2}\frac{1}{\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}}+2i\sqrt{3}(\frac{63}{-4{\mathit{\_}\mathit{a}}^6+12{\mathit{\_}\mathit{a}}^{4}a-12{\mathit{\_}\mathit{a}}^2{a}^2+320{\mathit{\_}\mathit{C}\mathit{1}}^3+4a^3}\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{a}^3+{\mathit{\_}\mathit{a}}^6-3{\mathit{\_}\mathit{a}}^{4}a+3{\mathit{\_}\mathit{a}}^2{a}^2-a^3){(-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3)}^2}+\frac{63{\mathit{\_}\mathit{a}}^6-189{\mathit{\_}\mathit{a}}^{4}a+189{\mathit{\_}\mathit{a}}^2{a}^2-63a^3}{4}\frac{1}{\sqrt[3]{(4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^6-12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{4}a+12\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{a}}^{4}a-3{\mathit{\_}\mathit{a}}^2{a}^2+80{\mathit{\_}\mathit{C}\mathit{1}}^3+a^3}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^2{a}^2-4\sqrt{5}\sqrt{\frac{\mathit{\_}\mathit{C}\m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