\[ \int \sqrt {2-3 x} \sqrt {-5+2 x} \sqrt {1+4 x} \, dx \]
Optimal antiderivative \[ \frac {121 \EllipticF \left (\frac {\sqrt {33}\, \sqrt {1+4 x}}{11}, \frac {\sqrt {3}}{3}\right ) \sqrt {66}\, \sqrt {5-2 x}}{108 \sqrt {-5+2 x}}+\frac {\left (1+4 x \right )^{\frac {3}{2}} \sqrt {2-3 x}\, \sqrt {-5+2 x}}{10}-\frac {847 \EllipticE \left (\frac {2 \sqrt {2-3 x}\, \sqrt {11}}{11}, \frac {i \sqrt {2}}{2}\right ) \sqrt {11}\, \sqrt {-5+2 x}}{270 \sqrt {5-2 x}}-\frac {22 \sqrt {2-3 x}\, \sqrt {-5+2 x}\, \sqrt {1+4 x}}{45} \]
command
integrate((2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {1}{90} \, {\left (36 \, x - 35\right )} \sqrt {4 \, x + 1} \sqrt {2 \, x - 5} \sqrt {-3 \, x + 2} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\sqrt {4 \, x + 1} \sqrt {2 \, x - 5} \sqrt {-3 \, x + 2}, x\right ) \]