\[ \int x^3 \text {CosIntegral}(b x) \, dx \]
Optimal antiderivative \[ \frac {x^{4} \cosineIntegral \! \left (b x \right )}{4}+\frac {3 \cos \! \left (b x \right )}{2 b^{4}}-\frac {3 x^{2} \cos \! \left (b x \right )}{4 b^{2}}+\frac {3 x \sin \! \left (b x \right )}{2 b^{3}}-\frac {x^{3} \sin \! \left (b x \right )}{4 b} \]
command
integrate(x^3*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
\[ \frac {1}{4} \, x^{4} \operatorname {Ci}\left (b x\right ) - \frac {3 \, {\left (b^{2} x^{2} - 2\right )} \cos \left (b x\right )}{4 \, b^{4}} - \frac {{\left (b^{3} x^{3} - 6 \, b x\right )} \sin \left (b x\right )}{4 \, b^{4}} \]