\[ \int \frac {1}{\left (3 i x+4 x^2\right )^{5/2}} \, dx \]
Optimal antiderivative \[ \frac {\frac {2 i}{9}+\frac {16 x}{27}}{\left (4 x^{2}+3 i x \right )^{\frac {3}{2}}}+\frac {\frac {64 i}{81}+\frac {512 x}{243}}{\sqrt {4 x^{2}+3 i x}} \]
command
integrate(1/(3*I*x+4*x^2)^(5/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {{\left (8 \, {\left (16 \, {\left (8 \, x + 9 i\right )} x - 27\right )} x + 27 i\right )} \sqrt {8 \, x^{2} + 2 \, \sqrt {16 \, x^{2} + 9} x} {\left (\frac {3 i \, x}{4 \, x^{2} + \sqrt {16 \, x^{4} + 9 \, x^{2}}} + 1\right )}}{243 \, {\left (4 \, x^{2} + 3 i \, x\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________