\[ \int \frac {(3+5 x)^{5/2}}{\sqrt {1-2 x} (2+3 x)^{9/2}} \, dx \]
Optimal antiderivative \[ -\frac {816622 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{6806835}-\frac {265648 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{6806835}+\frac {2 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}}{147 \left (2+3 x \right )^{\frac {7}{2}}}+\frac {676 \sqrt {1-2 x}\, \sqrt {3+5 x}}{15435 \left (2+3 x \right )^{\frac {5}{2}}}-\frac {101902 \sqrt {1-2 x}\, \sqrt {3+5 x}}{324135 \left (2+3 x \right )^{\frac {3}{2}}}+\frac {816622 \sqrt {1-2 x}\, \sqrt {3+5 x}}{2268945 \sqrt {2+3 x}} \]
command
integrate((3+5*x)^(5/2)/(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
\[ \frac {2 \, {\left (11024397 \, x^{3} + 18838881 \, x^{2} + 10645545 \, x + 1985537\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{2268945 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (25 \, x^{2} + 30 \, x + 9\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32}, x\right ) \]