\[ \int \frac {x}{\left (c x^2\right )^{3/2} (a+b x)^2} \, dx \]
Optimal antiderivative \[ -\frac {1}{a^{2} c \sqrt {c \,x^{2}}}-\frac {b x}{a^{2} c \left (b x +a \right ) \sqrt {c \,x^{2}}}-\frac {2 b x \ln \! \left (x \right )}{a^{3} c \sqrt {c \,x^{2}}}+\frac {2 b x \ln \! \left (b x +a \right )}{a^{3} c \sqrt {c \,x^{2}}} \]
command
integrate(x/(c*x^2)^(3/2)/(b*x+a)^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {Exception raised: TypeError} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \frac {\frac {2 \, b^{2} \log \left ({\left | -\frac {a}{b x + a} + 1 \right |}\right )}{a^{3} \mathrm {sgn}\left (-\frac {b}{b x + a} + \frac {a b}{{\left (b x + a\right )}^{2}}\right )} + \frac {b^{2}}{{\left (b x + a\right )} a^{2} \mathrm {sgn}\left (-\frac {b}{b x + a} + \frac {a b}{{\left (b x + a\right )}^{2}}\right )} - \frac {b^{2}}{a^{3} {\left (\frac {a}{b x + a} - 1\right )} \mathrm {sgn}\left (-\frac {b}{b x + a} + \frac {a b}{{\left (b x + a\right )}^{2}}\right )}}{b c^{\frac {3}{2}}} \]