\[ \int \frac {(2+3 x)^{3/2} (3+5 x)^{5/2}}{\sqrt {1-2 x}} \, dx \]
Optimal antiderivative \[ -\frac {8256877 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{170100}-\frac {62092 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{42525}-\frac {\left (2+3 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {5}{2}} \sqrt {1-2 x}}{9}-\frac {1877 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{630}-\frac {3 \left (3+5 x \right )^{\frac {5}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{7}-\frac {62092 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}{2835} \]
command
integrate((2+3*x)^(3/2)*(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
\[ -\frac {1}{5670} \, {\left (47250 \, x^{3} + 148950 \, x^{2} + 212175 \, x + 208073\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{2 \, x - 1}, x\right ) \]