\[ \int \frac {\sqrt {1-2 x} (3+5 x)^{5/2}}{(2+3 x)^{9/2}} \, dx \]
Optimal antiderivative \[ -\frac {173482 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{324135}+\frac {23612 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{324135}-\frac {118 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}}{735 \left (2+3 x \right )^{\frac {5}{2}}}-\frac {2 \left (3+5 x \right )^{\frac {5}{2}} \sqrt {1-2 x}}{21 \left (2+3 x \right )^{\frac {7}{2}}}-\frac {4282 \sqrt {1-2 x}\, \sqrt {3+5 x}}{15435 \left (2+3 x \right )^{\frac {3}{2}}}+\frac {173482 \sqrt {1-2 x}\, \sqrt {3+5 x}}{108045 \sqrt {2+3 x}} \]
command
integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^(9/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\left (2342007 \, x^{3} + 4290411 \, x^{2} + 2623695 \, x + 535637\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{108045 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\left (25 \, x^{2} + 30 \, x + 9\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32}, x\right ) \]