\[ \int \frac {\sqrt {2-3 x} (7+5 x)^3}{\sqrt {-5+2 x} \sqrt {1+4 x}} \, dx \]
Optimal antiderivative \[ -\frac {25260049 \EllipticF \left (\frac {\sqrt {33}\, \sqrt {1+4 x}}{11}, \frac {\sqrt {3}}{3}\right ) \sqrt {66}\, \sqrt {5-2 x}}{36288 \sqrt {-5+2 x}}+\frac {15629623 \EllipticE \left (\frac {2 \sqrt {2-3 x}\, \sqrt {11}}{11}, \frac {i \sqrt {2}}{2}\right ) \sqrt {11}\, \sqrt {-5+2 x}}{9072 \sqrt {5-2 x}}+\frac {110743 \sqrt {2-3 x}\, \sqrt {-5+2 x}\, \sqrt {1+4 x}}{864}+\frac {121 \left (7+5 x \right ) \sqrt {2-3 x}\, \sqrt {-5+2 x}\, \sqrt {1+4 x}}{24}+\frac {5 \left (7+5 x \right )^{2} \sqrt {2-3 x}\, \sqrt {-5+2 x}\, \sqrt {1+4 x}}{28} \]
command
integrate((7+5*x)^3*(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
\[ \frac {5}{6048} \, {\left (5400 \, x^{2} + 45612 \, x + 208313\right )} \sqrt {4 \, x + 1} \sqrt {2 \, x - 5} \sqrt {-3 \, x + 2} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\left (125 \, x^{3} + 525 \, x^{2} + 735 \, x + 343\right )} \sqrt {4 \, x + 1} \sqrt {2 \, x - 5} \sqrt {-3 \, x + 2}}{8 \, x^{2} - 18 \, x - 5}, x\right ) \]