\[ \int \frac {S(b x)}{x^5} \, dx \]
Optimal antiderivative \[ -\frac {b^{3} \pi \cos \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{12 x}-\frac {b^{4} \pi ^{2} \mathrm {S}\left (b x \right )}{12}-\frac {\mathrm {S}\left (b x \right )}{4 x^{4}}-\frac {b \sin \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{12 x^{3}} \]
command
integrate(fresnel_sin(b*x)/x^5,x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {\pi b^{3} x^{3} \cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) + b x \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) + {\left (\pi ^{2} b^{4} x^{4} + 3\right )} \operatorname {S}\left (b x\right )}{12 \, x^{4}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\rm fresnels}\left (b x\right )}{x^{5}}, x\right ) \]