\[ \int \frac {\text {FresnelC}(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right )}{x^2} \, dx \]
Optimal antiderivative \[ \frac {b \pi \FresnelC \left (b x \right )^{2}}{2}+\frac {b \sinIntegral \left (b^{2} \pi \,x^{2}\right )}{4}-\frac {\FresnelC \left (b x \right ) \sin \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{x} \]
command
integrate(fresnel_cos(b*x)*sin(1/2*b^2*pi*x^2)/x^2,x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, \pi b x \operatorname {C}\left (b x\right )^{2} + b x \operatorname {Si}\left (\pi b^{2} x^{2}\right ) - 4 \, \operatorname {C}\left (b x\right ) \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )}{4 \, x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\rm fresnelc}\left (b x\right ) \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )}{x^{2}}, x\right ) \]