\[ \int \frac {(7+5 x)^4}{\sqrt {2-3 x} \sqrt {-5+2 x} \sqrt {1+4 x}} \, dx \]
Optimal antiderivative \[ \frac {392989907 \EllipticF \left (\frac {\sqrt {33}\, \sqrt {1+4 x}}{11}, \frac {\sqrt {3}}{3}\right ) \sqrt {66}\, \sqrt {5-2 x}}{133056 \sqrt {-5+2 x}}-\frac {5109835 \EllipticE \left (\frac {2 \sqrt {2-3 x}\, \sqrt {11}}{11}, \frac {i \sqrt {2}}{2}\right ) \sqrt {11}\, \sqrt {-5+2 x}}{756 \sqrt {5-2 x}}-\frac {120355 \sqrt {2-3 x}\, \sqrt {-5+2 x}\, \sqrt {1+4 x}}{288}-\frac {305 \left (7+5 x \right ) \sqrt {2-3 x}\, \sqrt {-5+2 x}\, \sqrt {1+4 x}}{24}-\frac {25 \left (7+5 x \right )^{2} \sqrt {2-3 x}\, \sqrt {-5+2 x}\, \sqrt {1+4 x}}{84} \]
command
integrate((7+5*x)^4/(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
\[ -\frac {25}{2016} \, {\left (600 \, x^{2} + 6804 \, x + 42049\right )} \sqrt {4 \, x + 1} \sqrt {2 \, x - 5} \sqrt {-3 \, x + 2} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (625 \, x^{4} + 3500 \, x^{3} + 7350 \, x^{2} + 6860 \, x + 2401\right )} \sqrt {4 \, x + 1} \sqrt {2 \, x - 5} \sqrt {-3 \, x + 2}}{24 \, x^{3} - 70 \, x^{2} + 21 \, x + 10}, x\right ) \]