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