\[ \int \frac {\text {FresnelC}(b x)}{x^2} \, dx \]
Optimal antiderivative \[ \frac {b \cosineIntegral \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{2}-\frac {\FresnelC \left (b x \right )}{x} \]
command
integrate(fresnel_cos(b*x)/x^2,x, algorithm="maxima")
Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output
\[ \frac {1}{4} \, b {\left ({\rm Ei}\left (\frac {1}{2} i \, \pi b^{2} x^{2}\right ) + {\rm Ei}\left (-\frac {1}{2} i \, \pi b^{2} x^{2}\right )\right )} - \frac {\operatorname {C}\left (b x\right )}{x} \]
Maxima 5.44 via sagemath 9.3 output
\[ \int \frac {{\rm fresnelc}\left (b x\right )}{x^{2}}\,{d x} \]________________________________________________________________________________________