\[ \int \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2} \, dx \]
Optimal antiderivative \[ -\frac {1508889271 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{233887500}-\frac {11346991 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{58471875}-\frac {23 \left (2+3 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {5}{2}} \sqrt {1-2 x}}{2475}+\frac {2 \left (2+3 x \right )^{\frac {5}{2}} \left (3+5 x \right )^{\frac {5}{2}} \sqrt {1-2 x}}{55}-\frac {342971 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{866250}-\frac {543 \left (3+5 x \right )^{\frac {5}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{9625}-\frac {11346991 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}{3898125} \]
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
\[ \frac {1}{7796250} \, {\left (63787500 \, x^{4} + 156161250 \, x^{3} + 132234750 \, x^{2} + 29706255 \, x - 27010769\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left ({\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}, x\right ) \]