\[ \int \frac {\sin (c+d x)}{a+b \sin ^2(c+d x)} \, dx \]
Optimal antiderivative \[ -\frac {\arctanh \left (\frac {\cos \left (d x +c \right ) \sqrt {b}}{\sqrt {a +b}}\right )}{d \sqrt {b}\, \sqrt {a +b}} \]
command
integrate(sin(d*x+c)/(a+b*sin(d*x+c)**2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________