\[ \int \frac {1}{\sqrt {c+d x^3} \left (4 c+d x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {x F_{1}\left (\frac {1}{3}, \frac {1}{2}, 1, \frac {4}{3}, -\frac {d \,x^{3}}{c}, -\frac {d \,x^{3}}{4 c}\right ) \sqrt {1+\frac {d \,x^{3}}{c}}}{4 c \sqrt {d \,x^{3}+c}} \]
command
integrate(1/(d*x^3+4*c)/(d*x^3+c)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \text {output too large to display} \]
Fricas 1.3.7 via sagemath 9.3 output \[ {\rm integral}\left (\frac {\sqrt {d x^{3} + c}}{d^{2} x^{6} + 5 \, c d x^{3} + 4 \, c^{2}}, x\right ) \]