\[ \int \frac {1}{\left (3 i x+4 x^2\right )^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {\frac {2 i}{3}+\frac {16 x}{9}}{\sqrt {4 x^{2}+3 i x}} \]
command
integrate(1/(3*I*x+4*x^2)^(3/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {\sqrt {8 \, x^{2} + 2 \, \sqrt {16 \, x^{2} + 9} x} {\left (8 \, x + 3 i\right )} {\left (\frac {3 i \, x}{4 \, x^{2} + \sqrt {16 \, x^{4} + 9 \, x^{2}}} + 1\right )}}{9 \, {\left (4 \, x^{2} + 3 i \, x\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________