2.228   ODE No. 228

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  3. Maple input

\[ (4 y(x)+11 x-11) y'(x)-25 y(x)-8 x+62=0 \] Mathematica : cpu = 0.288393 (sec), leaf count = 3357

\[\left \{\left \{y(x)\to \frac {1}{4 \left (-\frac {\sqrt [3]{2} \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right )}{81 (9 x-1) \left (81 \cosh \left (\frac {3 c_1}{8}\right ) x^2+81 \sinh \left (\frac {3 c_1}{8}\right ) x^2-18 \cosh \left (\frac {3 c_1}{8}\right ) x-18 \sinh \left (\frac {3 c_1}{8}\right ) x+\cosh \left (\frac {3 c_1}{8}\right )+\sinh \left (\frac {3 c_1}{8}\right )-1\right ) \sqrt [3]{-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )+\sqrt {4 \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right ){}^3+\left (-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )-39366\right ){}^2}-39366}}+\frac {\sqrt [3]{-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )+\sqrt {4 \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right ){}^3+\left (-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )-39366\right ){}^2}-39366}}{81 \sqrt [3]{2} (9 x-1) \left (81 \cosh \left (\frac {3 c_1}{8}\right ) x^2+81 \sinh \left (\frac {3 c_1}{8}\right ) x^2-18 \cosh \left (\frac {3 c_1}{8}\right ) x-18 \sinh \left (\frac {3 c_1}{8}\right ) x+\cosh \left (\frac {3 c_1}{8}\right )+\sinh \left (\frac {3 c_1}{8}\right )-1\right )}+\frac {1}{3 (9 x-1)}\right )}-\frac {11 (x-1)}{4}\right \},\left \{y(x)\to \frac {1}{4 \left (\frac {\left (1+i \sqrt {3}\right ) \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right )}{81\ 2^{2/3} (9 x-1) \left (81 \cosh \left (\frac {3 c_1}{8}\right ) x^2+81 \sinh \left (\frac {3 c_1}{8}\right ) x^2-18 \cosh \left (\frac {3 c_1}{8}\right ) x-18 \sinh \left (\frac {3 c_1}{8}\right ) x+\cosh \left (\frac {3 c_1}{8}\right )+\sinh \left (\frac {3 c_1}{8}\right )-1\right ) \sqrt [3]{-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )+\sqrt {4 \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right ){}^3+\left (-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )-39366\right ){}^2}-39366}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )+\sqrt {4 \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right ){}^3+\left (-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )-39366\right ){}^2}-39366}}{162 \sqrt [3]{2} (9 x-1) \left (81 \cosh \left (\frac {3 c_1}{8}\right ) x^2+81 \sinh \left (\frac {3 c_1}{8}\right ) x^2-18 \cosh \left (\frac {3 c_1}{8}\right ) x-18 \sinh \left (\frac {3 c_1}{8}\right ) x+\cosh \left (\frac {3 c_1}{8}\right )+\sinh \left (\frac {3 c_1}{8}\right )-1\right )}+\frac {1}{3 (9 x-1)}\right )}-\frac {11 (x-1)}{4}\right \},\left \{y(x)\to \frac {1}{4 \left (\frac {\left (1-i \sqrt {3}\right ) \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right )}{81\ 2^{2/3} (9 x-1) \left (81 \cosh \left (\frac {3 c_1}{8}\right ) x^2+81 \sinh \left (\frac {3 c_1}{8}\right ) x^2-18 \cosh \left (\frac {3 c_1}{8}\right ) x-18 \sinh \left (\frac {3 c_1}{8}\right ) x+\cosh \left (\frac {3 c_1}{8}\right )+\sinh \left (\frac {3 c_1}{8}\right )-1\right ) \sqrt [3]{-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )+\sqrt {4 \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right ){}^3+\left (-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )-39366\right ){}^2}-39366}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )+\sqrt {4 \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right ){}^3+\left (-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )-39366\right ){}^2}-39366}}{162 \sqrt [3]{2} (9 x-1) \left (81 \cosh \left (\frac {3 c_1}{8}\right ) x^2+81 \sinh \left (\frac {3 c_1}{8}\right ) x^2-18 \cosh \left (\frac {3 c_1}{8}\right ) x-18 \sinh \left (\frac {3 c_1}{8}\right ) x+\cosh \left (\frac {3 c_1}{8}\right )+\sinh \left (\frac {3 c_1}{8}\right )-1\right )}+\frac {1}{3 (9 x-1)}\right )}-\frac {11 (x-1)}{4}\right \}\right \}\]

Maple : cpu = 0.3 (sec), leaf count = 377

\[ \left \{ y \left ( x \right ) ={\frac {22}{9}}+36\,{(9\,x-1) \left ( -1/27\,\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}}}-{\frac {16}{27\,\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}}}}}-{\frac {19}{27}}+2\,i\sqrt {3} \left ( {\frac {\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}}}}{54}}-{\frac {8}{27\,\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}}}}} \right ) \right ) \left ( -3\,\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}}}-48\,{\frac {1}{\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}}}}}+24+162\,i\sqrt {3} \left ( {\frac {\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}}}}{54}}-{\frac {8}{27\,\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}}}}} \right ) \right ) ^{-1}} \right \} \]