\[ \int \frac {1}{\sqrt {1+x^2} \sqrt {2+5 x^2}} \, dx \]
Optimal antiderivative \[ \frac {\sqrt {\frac {1}{x^{2}+1}}\, \EllipticF \left (\frac {x}{\sqrt {x^{2}+1}}, \frac {i \sqrt {6}}{2}\right ) \sqrt {5 x^{2}+2}\, \sqrt {2}}{2 \sqrt {\frac {5 x^{2}+2}{x^{2}+1}}} \]
command
integrate(1/(x^2+1)^(1/2)/(5*x^2+2)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {1}{2} i \, \sqrt {2} {\rm ellipticF}\left (i \, x, \frac {5}{2}\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {5 \, x^{2} + 2} \sqrt {x^{2} + 1}}{5 \, x^{4} + 7 \, x^{2} + 2}, x\right ) \]