\[ \int \frac {1}{(1-2 x)^{3/2} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx \]
Optimal antiderivative \[ \frac {2 \EllipticE \left (\sqrt {5}\, \sqrt {2+3 x}, \frac {\sqrt {70}}{35}\right ) \sqrt {35}\, \sqrt {-3-5 x}}{77 \sqrt {3+5 x}}+\frac {4 \sqrt {2+3 x}\, \sqrt {3+5 x}}{77 \sqrt {1-2 x}} \]
command
integrate(1/(1-2*x)^(3/2)/(2+3*x)^(1/2)/(3+5*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {4 \, \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{77 \, {\left (2 \, x - 1\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6}, x\right ) \]