\[ \int \frac {(2+3 x)^{11/2}}{(1-2 x)^{5/2} (3+5 x)^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {1508889271 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{49912500}-\frac {11346991 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{12478125}+\frac {7 \left (2+3 x \right )^{\frac {9}{2}}}{33 \left (1-2 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}-\frac {896 \left (2+3 x \right )^{\frac {7}{2}}}{363 \sqrt {1-2 x}\, \sqrt {3+5 x}}+\frac {4439 \left (2+3 x \right )^{\frac {5}{2}} \sqrt {1-2 x}}{19965 \sqrt {3+5 x}}-\frac {932783 \left (2+3 x \right )^{\frac {3}{2}} \sqrt {1-2 x}\, \sqrt {3+5 x}}{332750}-\frac {21713939 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}{1663750} \]
command
integrate((2+3*x)^(11/2)/(1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {{\left (48514950 \, x^{4} + 286777260 \, x^{3} - 1463754851 \, x^{2} - 376752444 \, x + 356556921\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{4991250 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{200 \, x^{5} - 60 \, x^{4} - 138 \, x^{3} + 47 \, x^{2} + 24 \, x - 9}, x\right ) \]