\[ \int \frac {-1+x}{\sqrt {-7+4 x+14 x^2-12 x^3+x^4}} \, dx \]
Optimal antiderivative \[ \ln \left (-1+x \right )-\ln \left (-5+6 x -x^{2}+\sqrt {x^{4}-12 x^{3}+14 x^{2}+4 x -7}\right ) \]
command
integrate((-1+x)/(x^4-12*x^3+14*x^2+4*x-7)^(1/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \log \left (4 \, \sqrt {2}\right ) \mathrm {sgn}\left (x - 1\right ) - \frac {\log \left ({\left | -x + \sqrt {x^{2} - 10 \, x - 7} + 5 \right |}\right )}{\mathrm {sgn}\left (x - 1\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \mathit {undef} \]________________________________________________________________________________________