\[ \int \frac {(2+3 x)^{5/2} (3+5 x)^{3/2}}{\sqrt {1-2 x}} \, dx \]
Optimal antiderivative \[ -\frac {44109377 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{1417500}-\frac {663409 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{708750}-\frac {137 \left (2+3 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}}{315}-\frac {\left (2+3 x \right )^{\frac {5}{2}} \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}}{9}-\frac {9547 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{5250}-\frac {663409 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}{47250} \]
command
integrate((2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {1}{47250} \, {\left (236250 \, x^{3} + 765000 \, x^{2} + 1114065 \, x + 1107478\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{2 \, x - 1}, x\right ) \]