\[ \int \cos ^{\frac {5}{2}}(c+d x) \sqrt {b \cos (c+d x)} \, dx \]
Optimal antiderivative \[ \frac {\sin \left (d x +c \right ) \sqrt {b \cos \left (d x +c \right )}}{d \sqrt {\cos \left (d x +c \right )}}-\frac {\left (\sin ^{3}\left (d x +c \right )\right ) \sqrt {b \cos \left (d x +c \right )}}{3 d \sqrt {\cos \left (d x +c \right )}} \]
command
integrate(cos(d*x+c)^(5/2)*(b*cos(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 \[ \text {Timed out} \]_______________________________________________________