\[ \int \frac {\text {sech}^2(x)}{\sqrt {-4+\tanh ^2(x)}} \, dx \]
Optimal antiderivative \[ \arctanh \left (\frac {\tanh \left (x \right )}{\sqrt {-4+\tanh ^{2}\left (x \right )}}\right ) \]
command
integrate(sech(x)^2/(-4+tanh(x)^2)^(1/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \log \left (\frac {8}{3} \, \sqrt {3} {\left (2 i \, \sqrt {3} - 3\right )} - 8 \, \sqrt {3} e^{\left (2 \, x\right )} + 8 \, \sqrt {3 \, e^{\left (4 \, x\right )} + 10 \, e^{\left (2 \, x\right )} + 3}\right ) - \log \left (\frac {8}{3} \, \sqrt {3} {\left (-2 i \, \sqrt {3} - 3\right )} - 8 \, \sqrt {3} e^{\left (2 \, x\right )} + 8 \, \sqrt {3 \, e^{\left (4 \, x\right )} + 10 \, e^{\left (2 \, x\right )} + 3}\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {\operatorname {sech}\left (x\right )^{2}}{\sqrt {\tanh \left (x\right )^{2} - 4}}\,{d x} \]________________________________________________________________________________________