\[ \int \frac {\sin ^3(a+b x)}{(d \cos (a+b x))^{11/2}} \, dx \]
Optimal antiderivative \[ \frac {2}{9 b d \left (d \cos \! \left (b x +a \right )\right )^{\frac {9}{2}}}-\frac {2}{5 b \,d^{3} \left (d \cos \! \left (b x +a \right )\right )^{\frac {5}{2}}} \]
command
integrate(sin(b*x+a)^3/(d*cos(b*x+a))^(11/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ -\frac {2 \, {\left (9 \, b^{5} d^{5} \cos \left (b x + a\right )^{2} - 5 \, b^{5} d^{5}\right )}}{45 \, \sqrt {d \cos \left (b x + a\right )} b^{6} d^{10} \cos \left (b x + a\right )^{4}} \]