\[ \int \frac {1}{\sqrt {-1-\cot ^2(x)}} \, dx \]
Optimal antiderivative \[ -\frac {\cot \! \left (x \right )}{\sqrt {-\left (\csc ^{2}\left (x \right )\right )}} \]
command
integrate(1/(-1-cot(x)**2)**(1/2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \int \frac {1}{\sqrt {- \cot ^{2}{\left (x \right )} - 1}}\, dx \]
Sympy 1.8 under Python 3.8.8 output
\[ - \frac {\cot {\left (x \right )}}{\sqrt {- \cot ^{2}{\left (x \right )} - 1}} \]