\[ \int \frac {\cos (c+d x)}{(a+b \sin (c+d x))^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {2}{b d \sqrt {a +b \sin \! \left (d x +c \right )}} \]
command
integrate(cos(d*x+c)/(a+b*sin(d*x+c))^(3/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {Timed out} \]
Giac 1.7.0 via sagemath 9.3 output
\[ -\frac {2}{\sqrt {b \sin \left (d x + c\right ) + a} b d} \]