\[ \int \frac {1}{\sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {1255552 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{17787}-\frac {37768 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{17787}+\frac {2 \sqrt {1-2 x}}{7 \left (2+3 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {3}{2}}}+\frac {428 \sqrt {1-2 x}}{49 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {2+3 x}}-\frac {94420 \sqrt {1-2 x}\, \sqrt {2+3 x}}{1617 \left (3+5 x \right )^{\frac {3}{2}}}+\frac {6277760 \sqrt {1-2 x}\, \sqrt {2+3 x}}{17787 \sqrt {3+5 x}} \]
command
integrate(1/(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
\[ \frac {2 \, {\left (141249600 \, x^{3} + 268408770 \, x^{2} + 169778606 \, x + 35747225\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{17787 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{6750 \, x^{7} + 22275 \, x^{6} + 27765 \, x^{5} + 13943 \, x^{4} - 883 \, x^{3} - 4014 \, x^{2} - 1620 \, x - 216}, x\right ) \]