\[ \int \frac {1}{\left (c+a^2 c x^2\right ) \text {ArcTan}(a x)} \, dx \]
Optimal antiderivative \[ \frac {\ln \left (\arctan \left (a x \right )\right )}{a c} \]
command
integrate(1/(a**2*c*x**2+c)/atan(a*x),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {\log {\left (\operatorname {atan}{\left (a x \right )} \right )}}{a c} \]
Sympy 1.8 under Python 3.8.8 output
\[ \begin {cases} \frac {\log {\left (\operatorname {atan}{\left (a x \right )} \right )}}{a c} & \text {for}\: c \neq 0 \\\tilde {\infty } \int \frac {1}{\operatorname {atan}{\left (a x \right )}}\, dx & \text {otherwise} \end {cases} \]________________________________________________________________________________________