\[ \int \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2} \, dx \]
Optimal antiderivative \[ -\frac {16416987253 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{608107500}-\frac {493825477 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{608107500}-\frac {23 \left (2+3 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {7}{2}} \sqrt {1-2 x}}{3575}+\frac {2 \left (2+3 x \right )^{\frac {5}{2}} \left (3+5 x \right )^{\frac {7}{2}} \sqrt {1-2 x}}{65}-\frac {1865989 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{1126125}-\frac {564731 \left (3+5 x \right )^{\frac {5}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{2252250}-\frac {2014 \left (3+5 x \right )^{\frac {7}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{53625}-\frac {493825477 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}{40540500} \]
command
integrate((2+3*x)^(5/2)*(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
\[ \frac {1}{40540500} \, {\left (1403325000 \, x^{5} + 4299277500 \, x^{4} + 5075689500 \, x^{3} + 2626854750 \, x^{2} + 139824180 \, x - 707313559\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left ({\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}, x\right ) \]