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