\[ \int \frac {S(b x)}{x^4} \, dx \]
Optimal antiderivative \[ \frac {b^{3} \pi \cosineIntegral \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{12}-\frac {\mathrm {S}\left (b x \right )}{3 x^{3}}-\frac {b \sin \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{6 x^{2}} \]
command
integrate(fresnel_sin(b*x)/x^4,x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {\pi b^{3} x^{3} \operatorname {Ci}\left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) + \pi b^{3} x^{3} \operatorname {Ci}\left (-\frac {1}{2} \, \pi b^{2} x^{2}\right ) - 4 \, b x \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) - 8 \, \operatorname {S}\left (b x\right )}{24 \, x^{3}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\rm fresnels}\left (b x\right )}{x^{4}}, x\right ) \]