\[ \int \frac {\sqrt {-1+x^2+x^5} \left (2+3 x^5\right )}{1+x^4-2 x^5+x^{10}} \, dx \]
Optimal antiderivative \[ -\sqrt {1+i}\, \arctan \left (\frac {\sqrt {-1-i}\, x}{\sqrt {x^{5}+x^{2}-1}}\right )-\sqrt {1-i}\, \arctan \left (\frac {\sqrt {-1+i}\, x}{\sqrt {x^{5}+x^{2}-1}}\right ) \]
command
Integrate[(Sqrt[-1 + x^2 + x^5]*(2 + 3*x^5))/(1 + x^4 - 2*x^5 + x^10),x]
Mathematica 13.1 output
\[ -\sqrt {1+i} \text {ArcTan}\left (\frac {\sqrt {-1-i} x}{\sqrt {-1+x^2+x^5}}\right )-\sqrt {1-i} \text {ArcTan}\left (\frac {\sqrt {-1+i} x}{\sqrt {-1+x^2+x^5}}\right ) \]
Mathematica 12.3 output
\[ \int \frac {\sqrt {-1+x^2+x^5} \left (2+3 x^5\right )}{1+x^4-2 x^5+x^{10}} \, dx \]________________________________________________________________________________________