2.1 Problem number 514

\[ \int \frac {\left (2+x^3\right ) \sqrt {-1+x^2+x^3}}{\left (-1+x^3\right )^2} \, dx \]

Optimal antiderivative \[ -\frac {x \sqrt {x^{3}+x^{2}-1}}{x^{3}-1}-\operatorname {arctanh}\left (\frac {x}{\sqrt {x^{3}+x^{2}-1}}\right ) \]

command

Int[((2 + x^3)*Sqrt[-1 + x^2 + x^3])/(-1 + x^3)^2,x]

Rubi 4.17.3 under Mathematica 13.3.1 output

\[ \text {output too large to display} \]

Rubi 4.16.1 under Mathematica 13.3.1 output \[ \text {\$Aborted} \]__________________________________________