\[ \int \frac {(3+5 x)^{3/2}}{\sqrt {1-2 x} (2+3 x)^{9/2}} \, dx \]
Optimal antiderivative \[ -\frac {184636 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{756315}-\frac {9124 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{756315}+\frac {2 \sqrt {1-2 x}\, \sqrt {3+5 x}}{147 \left (2+3 x \right )^{\frac {7}{2}}}-\frac {536 \sqrt {1-2 x}\, \sqrt {3+5 x}}{5145 \left (2+3 x \right )^{\frac {5}{2}}}+\frac {974 \sqrt {1-2 x}\, \sqrt {3+5 x}}{36015 \left (2+3 x \right )^{\frac {3}{2}}}+\frac {184636 \sqrt {1-2 x}\, \sqrt {3+5 x}}{252105 \sqrt {2+3 x}} \]
command
integrate((3+5*x)^(3/2)/(2+3*x)^(9/2)/(1-2*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\left (2492586 \, x^{3} + 5015853 \, x^{2} + 3324960 \, x + 727631\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{252105 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (5 \, x + 3\right )}^{\frac {3}{2}} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32}, x\right ) \]