\[ \int \frac {\text {FresnelC}(b x)}{x^4} \, dx \]
Optimal antiderivative \[ -\frac {b \cos \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{6 x^{2}}-\frac {\FresnelC \left (b x \right )}{3 x^{3}}-\frac {b^{3} \pi \sinIntegral \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{12} \]
command
integrate(fresnel_cos(b*x)/x^4,x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {\pi b^{3} x^{3} \operatorname {Si}\left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) + 2 \, b x \cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) + 4 \, \operatorname {C}\left (b x\right )}{12 \, x^{3}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\rm fresnelc}\left (b x\right )}{x^{4}}, x\right ) \]