\[ \int x \text {CosIntegral}(b x) \, dx \]
Optimal antiderivative \[ \frac {x^{2} \cosineIntegral \! \left (b x \right )}{2}-\frac {\cos \! \left (b x \right )}{2 b^{2}}-\frac {x \sin \! \left (b x \right )}{2 b} \]
command
integrate(x*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
\[ \frac {1}{2} \, x^{2} \operatorname {Ci}\left (b x\right ) - \frac {x \sin \left (b x\right )}{2 \, b} - \frac {\cos \left (b x\right )}{2 \, b^{2}} \]