\[ \int \frac {a+b x}{(c+d x) (e+f x) (g+h x)} \, dx \]
Optimal antiderivative \[ -\frac {\left (-a d +b c \right ) \ln \left (d x +c \right )}{\left (-c f +d e \right ) \left (-c h +d g \right )}+\frac {\left (-a f +b e \right ) \ln \left (f x +e \right )}{\left (-c f +d e \right ) \left (-e h +f g \right )}-\frac {\left (-a h +b g \right ) \ln \left (h x +g \right )}{\left (-c h +d g \right ) \left (-e h +f g \right )} \]
command
integrate((b*x+a)/(d*x+c)/(f*x+e)/(h*x+g),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {{\left ({\left (b c - a d\right )} f g - {\left (b c - a d\right )} h e\right )} \log \left (d x + c\right ) + {\left (a d f g - a c f h - {\left (b d g - b c h\right )} e\right )} \log \left (f x + e\right ) - {\left (b c f g - a c f h - {\left (b d g - a d h\right )} e\right )} \log \left (h x + g\right )}{c d f^{2} g^{2} - c^{2} f^{2} g h + {\left (d^{2} g h - c d h^{2}\right )} e^{2} - {\left (d^{2} f g^{2} - c^{2} f h^{2}\right )} e} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ \text {Timed out} \]