\[ \int \frac {(2+3 x)^{7/2} (3+5 x)^{5/2}}{\sqrt {1-2 x}} \, dx \]
Optimal antiderivative \[ -\frac {610627101631 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{1216215000}-\frac {2295970088 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{152026875}-\frac {14303 \left (2+3 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {5}{2}} \sqrt {1-2 x}}{12870}-\frac {41 \left (2+3 x \right )^{\frac {5}{2}} \left (3+5 x \right )^{\frac {5}{2}} \sqrt {1-2 x}}{143}-\frac {\left (2+3 x \right )^{\frac {7}{2}} \left (3+5 x \right )^{\frac {5}{2}} \sqrt {1-2 x}}{13}-\frac {138809831 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{4504500}-\frac {221673 \left (3+5 x \right )^{\frac {5}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{50050}-\frac {2295970088 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}{10135125} \]
command
integrate((2+3*x)^(7/2)*(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
\[ -\frac {1}{40540500} \, {\left (2104987500 \, x^{5} + 9351247500 \, x^{4} + 18620894250 \, x^{3} + 22592085750 \, x^{2} + 19961825445 \, x + 16001700059\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{2 \, x - 1}, x\right ) \]