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