\[ \int \frac {1}{\sqrt {3-2 \tan (c+d x)} \sqrt {\tan (c+d x)}} \, dx \]
Optimal antiderivative \[ \frac {\arctan \left (\frac {\sqrt {2-3 i}\, \left (\sqrt {\tan }\left (d x +c \right )\right )}{\sqrt {3-2 \tan \left (d x +c \right )}}\right )}{d \sqrt {2-3 i}}+\frac {\arctan \left (\frac {\sqrt {2+3 i}\, \left (\sqrt {\tan }\left (d x +c \right )\right )}{\sqrt {3-2 \tan \left (d x +c \right )}}\right )}{d \sqrt {2+3 i}} \]
command
integrate(1/(3-2*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \int \frac {1}{\sqrt {-2 \, \tan \left (d x + c\right ) + 3} \sqrt {\tan \left (d x + c\right )}}\,{d x} \]_______________________________________________________