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