\[ \int \frac {(2+3 x)^{9/2}}{\sqrt {1-2 x} (3+5 x)^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {6515539 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{11343750}-\frac {104663 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{5671875}-\frac {2 \left (2+3 x \right )^{\frac {7}{2}} \sqrt {1-2 x}}{165 \left (3+5 x \right )^{\frac {3}{2}}}-\frac {668 \left (2+3 x \right )^{\frac {5}{2}} \sqrt {1-2 x}}{9075 \sqrt {3+5 x}}+\frac {403 \left (2+3 x \right )^{\frac {3}{2}} \sqrt {1-2 x}\, \sqrt {3+5 x}}{75625}-\frac {87476 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}{378125} \]
command
integrate((2+3*x)^(9/2)/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {{\left (3675375 \, x^{3} + 13721400 \, x^{2} + 12517925 \, x + 3365042\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{1134375 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{250 \, x^{4} + 325 \, x^{3} + 45 \, x^{2} - 81 \, x - 27}, x\right ) \]