\[ \int x^2 \text {CosIntegral}(b x) \, dx \]
Optimal antiderivative \[ \frac {x^{3} \cosineIntegral \left (b x \right )}{3}-\frac {2 x \cos \left (b x \right )}{3 b^{2}}+\frac {2 \sin \left (b x \right )}{3 b^{3}}-\frac {x^{2} \sin \left (b x \right )}{3 b} \]
command
integrate(x^2*fresnel_cos(b*x),x, algorithm="maxima")
Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output
\[ \frac {1}{3} \, x^{3} \operatorname {C}\left (b x\right ) - \frac {\pi b^{2} x^{2} \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) + 2 \, \cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )}{3 \, \pi ^{2} b^{3}} \]
Maxima 5.44 via sagemath 9.3 output
\[ \int x^{2} {\rm Ci}\left (b x\right )\,{d x} \]________________________________________________________________________________________