\[ \int \frac {-\sqrt {-4+x}-4 \sqrt {-1+x}+\sqrt {-4+x} x+\sqrt {-1+x} x}{\left (1+\sqrt {-4+x}+\sqrt {-1+x}\right ) \left (4-5 x+x^2\right )} \, dx \]
Optimal antiderivative \[ 2 \ln \left (1+\sqrt {-4+x}+\sqrt {-1+x}\right ) \]
command
integrate((-(-4+x)**(1/2)+x*(-4+x)**(1/2)-4*(-1+x)**(1/2)+x*(-1+x)**(1/2))/(x**2-5*x+4)/(1+(-4+x)**(1/2)+(-1+x)**(1/2)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ 2 \log {\left (\sqrt {x - 4} + \sqrt {x - 1} + 1 \right )} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________