\[ \int \frac {S(b x)}{x^4} \, dx \]
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="maxima")
Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output
\[ \frac {1}{24} \, {\left (\pi \Gamma \left (-1, \frac {1}{2} i \, \pi b^{2} x^{2}\right ) + \pi \Gamma \left (-1, -\frac {1}{2} i \, \pi b^{2} x^{2}\right )\right )} b^{3} - \frac {\operatorname {S}\left (b x\right )}{3 \, x^{3}} \]
Maxima 5.44 via sagemath 9.3 output
\[ \int \frac {{\rm fresnels}\left (b x\right )}{x^{4}}\,{d x} \]________________________________________________________________________________________