3.538   ODE No. 538

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

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

Mathematica: cpu = 0 (sec), leaf count = 0 $$\text{Hanged}$$

Maple: cpu = 0.608 (sec), leaf count = 3181 $$\{{\int }_{\mathit{\_}\mathit{b}}^x-\frac{1}{\mathit{\_}\mathit{a}}(6^{\frac{2}{3}}{\left(y\left(x\right)(\sqrt{3}\sqrt{\frac{y\left(x\right)(27\mathit{\_}\mathit{a}y\left(x\right)-2)}{\mathit{\_}\mathit{a}}}-9y\left(x\right)){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}-6y\left(x\right)\mathit{\_}\mathit{a}\sqrt[3]{6}\sqrt[3]{y\left(x\right)(\sqrt{3}\sqrt{\frac{y\left(x\right)(27\mathit{\_}\mathit{a}y\left(x\right)-2)}{\mathit{\_}\mathit{a}}}-9y\left(x\right)){\mathit{\_}\mathit{a}}^2}+6\mathit{\_}\mathit{a}y\left(x\right)){(6^{\frac{2}{3}}{\left(y\left(x\right)(\sqrt{3}\sqrt{\frac{y\left(x\right)(27\mathit{\_}\mathit{a}y\left(x\right)-2)}{\mathit{\_}\mathit{a}}}-9y\left(x\right)){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}+6\mathit{\_}\mathit{a}y\left(x\right))}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}6x\sqrt[3]{6}\sqrt[3]{\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27x\mathit{\_}\mathit{f}-2)}{x}}-9\mathit{\_}\mathit{f})x^2}{(6^{2/3}{\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27x\mathit{\_}\mathit{f}-2)}{x}}-9\mathit{\_}\mathit{f})x^2\right)}^{2/3}+6x\mathit{\_}\mathit{f})}^{-1}-{\int }_{\mathit{\_}\mathit{b}}^x-\frac{1}{\mathit{\_}\mathit{a}}(\frac{26^{2/3}}{3}((\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{f}(\frac{\sqrt{3}}{2}(\frac{27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2}{\mathit{\_}\mathit{a}}+27\mathit{\_}\mathit{f})\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}}-9){\mathit{\_}\mathit{a}}^2)\frac{1}{\sqrt[3]{\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2}}-6\mathit{\_}\mathit{a}\sqrt[3]{6}\sqrt[3]{\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2}-2\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}\sqrt[3]{6}((\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{f}(1/2\sqrt{3}(\frac{27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2}{\mathit{\_}\mathit{a}}+27\mathit{\_}\mathit{f})\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}}-9){\mathit{\_}\mathit{a}}^2){\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2\right)}^{-2/3}+6\mathit{\_}\mathit{a}){(6^{\frac{2}{3}}{\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}+6\mathit{\_}\mathit{a}\mathit{\_}\mathit{f})}^{-1}+\frac{1}{\mathit{\_}\mathit{a}}(6^{\frac{2}{3}}{\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}-6\mathit{\_}\mathit{f}\mathit{\_}\mathit{a}\sqrt[3]{6}\sqrt[3]{\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2}+6\mathit{\_}\mathit{a}\mathit{\_}\mathit{f})(\frac{26^{2/3}}{3}((\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{f}(\frac{\sqrt{3}}{2}(\frac{27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2}{\mathit{\_}\mathit{a}}+27\mathit{\_}\mathit{f})\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}}-9){\mathit{\_}\mathit{a}}^2)\frac{1}{\sqrt[3]{\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2}}+6\mathit{\_}\mathit{a}){(6^{\frac{2}{3}}{\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}+6\mathit{\_}\mathit{a}\mathit{\_}\mathit{f})}^{-2}\mathrm{d}\mathit{\_}\mathit{a}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0,{\int }_{\mathit{\_}\mathit{b}}^x-\frac{1}{\mathit{\_}\mathit{a}}(i\sqrt{3}{6}^{\frac{2}{3}}{\left(y\left(x\right)(\sqrt{3}\sqrt{\frac{y\left(x\right)(27\mathit{\_}\mathit{a}y\left(x\right)-2)}{\mathit{\_}\mathit{a}}}-9y\left(x\right)){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}-6i\sqrt{3}\mathit{\_}\mathit{a}y\left(x\right)-6^{\frac{2}{3}}{\left(y\left(x\right)(\sqrt{3}\sqrt{\frac{y\left(x\right)(27\mathit{\_}\mathit{a}y\left(x\right)-2)}{\mathit{\_}\mathit{a}}}-9y\left(x\right)){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}-12y\left(x\right)\mathit{\_}\mathit{a}\sqrt[3]{6}\sqrt[3]{y\left(x\right)(\sqrt{3}\sqrt{\frac{y\left(x\right)(27\mathit{\_}\mathit{a}y\left(x\right)-2)}{\mathit{\_}\mathit{a}}}-9y\left(x\right)){\mathit{\_}\mathit{a}}^2}-6\mathit{\_}\mathit{a}y\left(x\right)){(i\sqrt{3}{6}^{\frac{2}{3}}{\left(y\left(x\right)(\sqrt{3}\sqrt{\frac{y\left(x\right)(27\mathit{\_}\mathit{a}y\left(x\right)-2)}{\mathit{\_}\mathit{a}}}-9y\left(x\right)){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}-6i\sqrt{3}\mathit{\_}\mathit{a}y\left(x\right)-6^{\frac{2}{3}}{\left(y\left(x\right)(\sqrt{3}\sqrt{\frac{y\left(x\right)(27\mathit{\_}\mathit{a}y\left(x\right)-2)}{\mathit{\_}\mathit{a}}}-9y\left(x\right)){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}-6\mathit{\_}\mathit{a}y\left(x\right))}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}12x\sqrt[3]{6}\sqrt[3]{\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27x\mathit{\_}\mathit{f}-2)}{x}}-9\mathit{\_}\mathit{f})x^2}{(i\sqrt{3}{6}^{2/3}{\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27x\mathit{\_}\mathit{f}-2)}{x}}-9\mathit{\_}\mathit{f})x^2\right)}^{2/3}-6i\sqrt{3}x\mathit{\_}\mathit{f}-6^{2/3}{\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27x\mathit{\_}\mathit{f}-2)}{x}}-9\mathit{\_}\mathit{f})x^2\right)}^{2/3}-6x\mathit{\_}\mathit{f})}^{-1}-{\int }_{\mathit{\_}\mathit{b}}^x-\frac{1}{\mathit{\_}\mathit{a}}(\frac{2i}{3}\sqrt{3}{6}^{\frac{2}{3}}((\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{f}(\frac{\sqrt{3}}{2}(\frac{27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2}{\mathit{\_}\mathit{a}}+27\mathit{\_}\mathit{f})\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}}-9){\mathit{\_}\mathit{a}}^2)\frac{1}{\sqrt[3]{\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2}}-6i\sqrt{3}\mathit{\_}\mathit{a}-\frac{26^{2/3}}{3}((\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{f}(\frac{\sqrt{3}}{2}(\frac{27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2}{\mathit{\_}\mathit{a}}+27\mathit{\_}\mathit{f})\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}}-9){\mathit{\_}\mathit{a}}^2)\frac{1}{\sqrt[3]{\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2}}-12\mathit{\_}\mathit{a}\sqrt[3]{6}\sqrt[3]{\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2}-4\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}\sqrt[3]{6}((\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{f}(1/2\sqrt{3}(\frac{27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2}{\mathit{\_}\mathit{a}}+27\mathit{\_}\mathit{f})\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}}-9){\mathit{\_}\mathit{a}}^2){\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2\right)}^{-2/3}-6\mathit{\_}\mathit{a}){(i\sqrt{3}{6}^{\frac{2}{3}}{\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}-6i\sqrt{3}\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-6^{\frac{2}{3}}{\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}-6\mathit{\_}\mathit{a}\mathit{\_}\mathit{f})}^{-1}+\frac{1}{\mathit{\_}\mathit{a}}(i\sqrt{3}{6}^{\frac{2}{3}}{\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}-6i\sqrt{3}\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-6^{\frac{2}{3}}{\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}-12\mathit{\_}\mathit{f}\mathit{\_}\mathit{a}\sqrt[3]{6}\sqrt[3]{\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2}-6\mathit{\_}\mathit{a}\mathit{\_}\mathit{f})(\frac{2i}{3}\sqrt{3}{6}^{\frac{2}{3}}((\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{f}(\frac{\sqrt{3}}{2}(\frac{27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2}{\mathit{\_}\mathit{a}}+27\mathit{\_}\mathit{f})\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}}-9){\mathit{\_}\mathit{a}}^2)\frac{1}{\sqrt[3]{\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2}}-6i\sqrt{3}\mathit{\_}\mathit{a}-\frac{26^{2/3}}{3}((\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}{\mathit{\_}\mathit{a}}}-9\mathit{\_}\mathit{f}){\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{f}(\frac{\sqrt{3}}{2}(\frac{27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2}{\mathit{\_}\mathit{a}}+27\mathit{\_}\mathit{f})\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{f}(27\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}-2)}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}_{\mathit{\_}\mathit{b}}^x-\frac{1}{\mathit{\_}\mathit{a}}(i\sqrt{3}{6}^{\frac{2}{3}}{\left(y\left(x\right)(\sqrt{3}\sqrt{\frac{y\left(x\right)(27\mathit{\_}\mathit{a}y\left(x\right)-2)}{\mathit{\_}\mathit{a}}}-9y\left(x\right)){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}-6i\sqrt{3}\mathit{\_}\mathit{a}y\left(x\right)+6^{\frac{2}{3}}{\left(y\left(x\right)(\sqrt{3}\sqrt{\frac{y\left(x\right)(27\mathit{\_}\mathit{a}y\left(x\right)-2)}{\mathit{\_}\mathit{a}}}-9y\left(x\right)){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}+12y\left(x\right)\mathit{\_}\mathit{a}\sqrt[3]{6}\sqrt[3]{y\left(x\right)(\sqrt{3}\sqrt{\frac{y\left(x\right)(27\mathit{\_}\mathit{a}y\left(x\right)-2)}{\mathit{\_}\mathit{a}}}-9y\left(x\right)){\mathit{\_}\mathit{a}}^2}+6\mathit{\_}\mathit{a}y\left(x\right)){(i\sqrt{3}{6}^{\frac{2}{3}}{\left(y\left(x\right)(\sqrt{3}\sqrt{\frac{y\left(x\right)(27\mathit{\_}\mathit{a}y\left(x\right)-2)}{\mathit{\_}\mathit{a}}}-9y\left(x\right)){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}-6i\sqrt{3}\mathit{\_}\mathit{a}y\left(x\right)+6^{\frac{2}{3}}{\left(y\left(x\right)(\sqrt{3}\sqrt{\frac{y\left(x\right)(27\mathit{\_}\mathit{a}y\left(x\right)-2)}{\mathit{\_}\mathit{a}}}-9y\left(x\right)){\mathit{\_}\mathit{a}}^2\right)}^{\frac{2}{3}}+6\mathit{\_}\mathit{a}y\left(x\right))}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}-12x\sqrt[3]{6}\sqrt[3]{\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27x\mathit{\_}\mathit{f}-2)}{x}}-9\mathit{\_}\mathit{f})x^2}{(i\sqrt{3}{6}^{2/3}{\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27x\mathit{\_}\mathit{f}-2)}{x}}-9\mathit{\_}\mathit{f})x^2\right)}^{2/3}-6i\sqrt{3}x\mathit{\_}\mathit{f}+6^{2/3}{\left(\mathit{\_}\mathit{f}(\sqrt{3}\sqrt{\frac{\mathit{\_}\mathit{f}(27x\mathit{\_}\mathit{f}-2)}{x}}-9\mathit{\_}\mathit{f})x^2\right)}^{2/3}+6x\mathit{\_}\mathit{f})}^{-1}-{\int 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