\[ \int x^2 \text {CosIntegral}(b x) \, dx \]
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="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \frac {1}{3} \, x^{3} \operatorname {Ci}\left (b x\right ) - \frac {2 \, x \cos \left (b x\right )}{3 \, b^{2}} - \frac {{\left (b^{2} x^{2} - 2\right )} \sin \left (b x\right )}{3 \, b^{3}} \]