\[ \int \cos ^{\frac {3}{2}}(c+d x) (b \cos (c+d x))^{3/2} \, dx \]
Optimal antiderivative \[ \frac {b \sin \left (d x +c \right ) \sqrt {b \cos \left (d x +c \right )}}{d \sqrt {\cos \left (d x +c \right )}}-\frac {b \left (\sin ^{3}\left (d x +c \right )\right ) \sqrt {b \cos \left (d x +c \right )}}{3 d \sqrt {\cos \left (d x +c \right )}} \]
command
integrate(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^(3/2),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 \[ \text {Timed out} \]_______________________________________________________