\[ \int \frac {\sqrt {2-3 x} \sqrt {1+4 x} (7+5 x)}{\sqrt {-5+2 x}} \, dx \]
Optimal antiderivative \[ -\frac {4543 \EllipticF \left (\frac {\sqrt {33}\, \sqrt {1+4 x}}{11}, \frac {\sqrt {3}}{3}\right ) \sqrt {66}\, \sqrt {5-2 x}}{216 \sqrt {-5+2 x}}+\frac {\left (1+4 x \right )^{\frac {3}{2}} \sqrt {2-3 x}\, \sqrt {-5+2 x}}{4}+\frac {1397 \EllipticE \left (\frac {2 \sqrt {2-3 x}\, \sqrt {11}}{11}, \frac {i \sqrt {2}}{2}\right ) \sqrt {11}\, \sqrt {-5+2 x}}{27 \sqrt {5-2 x}}+\frac {95 \sqrt {2-3 x}\, \sqrt {-5+2 x}\, \sqrt {1+4 x}}{18} \]
command
integrate((7+5*x)*(2-3*x)^(1/2)*(1+4*x)^(1/2)/(-5+2*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {1}{36} \, {\left (36 \, x + 199\right )} \sqrt {4 \, x + 1} \sqrt {2 \, x - 5} \sqrt {-3 \, x + 2} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\left (5 \, x + 7\right )} \sqrt {4 \, x + 1} \sqrt {-3 \, x + 2}}{\sqrt {2 \, x - 5}}, x\right ) \]