79.21 Problem number 251

\[ \int \cos (a+b x) \cot ^2(c+b x) \, dx \]

Optimal antiderivative \[ -\frac {\cos \left (a -c \right ) \csc \left (b x +c \right )}{b}+\frac {\arctanh \left (\cos \left (b x +c \right )\right ) \sin \left (a -c \right )}{b}-\frac {\sin \left (b x +a \right )}{b} \]

command

integrate(cos(b*x+a)*cot(b*x+c)^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 \[ \text {Exception raised: NotImplementedError} \]_______________________________________________________