\[ \int \frac {\sqrt {3+5 x}}{\sqrt {1-2 x} (2+3 x)^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {2 \EllipticE \left (\sqrt {5}\, \sqrt {2+3 x}, \frac {\sqrt {70}}{35}\right ) \sqrt {35}\, \sqrt {-3-5 x}}{21 \sqrt {3+5 x}}-\frac {2 \sqrt {1-2 x}\, \sqrt {3+5 x}}{7 \sqrt {2+3 x}} \]
command
integrate((3+5*x)^(1/2)/(2+3*x)^(3/2)/(1-2*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {2 \, \sqrt {5 \, x + 3} \sqrt {-2 \, x + 1}}{7 \, \sqrt {3 \, x + 2}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4}, x\right ) \]