\[ \int \frac {\text {FresnelC}(b x)}{x^4} \, dx \]
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="maxima")
Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output
\[ -\frac {1}{24} \, {\left (i \, \pi \Gamma \left (-1, \frac {1}{2} i \, \pi b^{2} x^{2}\right ) - i \, \pi \Gamma \left (-1, -\frac {1}{2} i \, \pi b^{2} x^{2}\right )\right )} b^{3} - \frac {\operatorname {C}\left (b x\right )}{3 \, x^{3}} \]
Maxima 5.44 via sagemath 9.3 output
\[ \int \frac {{\rm fresnelc}\left (b x\right )}{x^{4}}\,{d x} \]________________________________________________________________________________________