\[ \int \frac {S(b x)}{x^3} \, dx \]
Optimal antiderivative \[ \frac {b^{2} \pi \FresnelC \left (b x \right )}{2}-\frac {\mathrm {S}\left (b x \right )}{2 x^{2}}-\frac {b \sin \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{2 x} \]
command
integrate(fresnel_sin(b*x)/x^3,x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {\pi \sqrt {b^{2}} b x^{2} \operatorname {C}\left (\sqrt {b^{2}} x\right ) - b x \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) - \operatorname {S}\left (b x\right )}{2 \, x^{2}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\rm fresnels}\left (b x\right )}{x^{3}}, x\right ) \]