\[ \int \frac {5-x}{(3+2 x)^{7/2} \sqrt {2+5 x+3 x^2}} \, dx \]
Optimal antiderivative \[ \frac {4501 \EllipticE \left (\sqrt {1+x}\, \sqrt {3}, \frac {i \sqrt {6}}{3}\right ) \sqrt {-3 x^{2}-5 x -2}\, \sqrt {3}}{1875 \sqrt {3 x^{2}+5 x +2}}-\frac {391 \EllipticF \left (\sqrt {1+x}\, \sqrt {3}, \frac {i \sqrt {6}}{3}\right ) \sqrt {-3 x^{2}-5 x -2}\, \sqrt {3}}{375 \sqrt {3 x^{2}+5 x +2}}-\frac {26 \sqrt {3 x^{2}+5 x +2}}{25 \left (3+2 x \right )^{\frac {5}{2}}}-\frac {782 \sqrt {3 x^{2}+5 x +2}}{375 \left (3+2 x \right )^{\frac {3}{2}}}-\frac {9002 \sqrt {3 x^{2}+5 x +2}}{1875 \sqrt {3+2 x}} \]
command
integrate((5-x)/(3+2*x)^(7/2)/(3*x^2+5*x+2)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {18413 \, \sqrt {6} {\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )} {\rm weierstrassPInverse}\left (\frac {19}{27}, -\frac {28}{729}, x + \frac {19}{18}\right ) - 81018 \, \sqrt {6} {\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )} {\rm weierstrassZeta}\left (\frac {19}{27}, -\frac {28}{729}, {\rm weierstrassPInverse}\left (\frac {19}{27}, -\frac {28}{729}, x + \frac {19}{18}\right )\right ) - 36 \, {\left (18004 \, x^{2} + 57922 \, x + 47349\right )} \sqrt {3 \, x^{2} + 5 \, x + 2} \sqrt {2 \, x + 3}}{33750 \, {\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {3 \, x^{2} + 5 \, x + 2} \sqrt {2 \, x + 3} {\left (x - 5\right )}}{48 \, x^{6} + 368 \, x^{5} + 1160 \, x^{4} + 1920 \, x^{3} + 1755 \, x^{2} + 837 \, x + 162}, x\right ) \]