\[ \int \frac {1}{(1-2 x)^{5/2} (2+3 x)^{7/2} \sqrt {3+5 x}} \, dx \]
Optimal antiderivative \[ -\frac {26062156 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{30504705}-\frac {837304 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{30504705}+\frac {4 \sqrt {3+5 x}}{231 \left (1-2 x \right )^{\frac {3}{2}} \left (2+3 x \right )^{\frac {5}{2}}}+\frac {1336 \sqrt {3+5 x}}{17787 \left (2+3 x \right )^{\frac {5}{2}} \sqrt {1-2 x}}-\frac {806 \sqrt {1-2 x}\, \sqrt {3+5 x}}{207515 \left (2+3 x \right )^{\frac {5}{2}}}+\frac {349904 \sqrt {1-2 x}\, \sqrt {3+5 x}}{1452605 \left (2+3 x \right )^{\frac {3}{2}}}+\frac {26062156 \sqrt {1-2 x}\, \sqrt {3+5 x}}{10168235 \sqrt {2+3 x}} \]
command
integrate(1/(1-2*x)^(5/2)/(2+3*x)^(7/2)/(3+5*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\left (1407356424 \, x^{4} + 513206712 \, x^{3} - 914077314 \, x^{2} - 176797172 \, x + 165071409\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{30504705 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{3240 \, x^{8} + 5724 \, x^{7} + 378 \, x^{6} - 4179 \, x^{5} - 1547 \, x^{4} + 1008 \, x^{3} + 504 \, x^{2} - 80 \, x - 48}, x\right ) \]