\[ \int \frac {(2+3 x)^{9/2}}{(1-2 x)^{5/2} (3+5 x)^{5/2}} \, dx \]
Optimal antiderivative \[ \frac {7 \left (2+3 x \right )^{\frac {7}{2}}}{33 \left (1-2 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {3}{2}}}-\frac {4971289 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{10980750}-\frac {76163 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{5490375}-\frac {140 \left (2+3 x \right )^{\frac {5}{2}}}{121 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}}+\frac {2063 \left (2+3 x \right )^{\frac {3}{2}} \sqrt {1-2 x}}{19965 \left (3+5 x \right )^{\frac {3}{2}}}+\frac {70226 \sqrt {1-2 x}\, \sqrt {2+3 x}}{1098075 \sqrt {3+5 x}} \]
command
integrate((2+3*x)^(9/2)/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {{\left (31924075 \, x^{3} + 30619782 \, x^{2} + 2244393 \, x - 2780992\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{1098075 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{1000 \, x^{6} + 300 \, x^{5} - 870 \, x^{4} - 179 \, x^{3} + 261 \, x^{2} + 27 \, x - 27}, x\right ) \]