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