\[ \int x^3 \cos (b x) \text {Si}(b x) \, dx \]
Optimal antiderivative \[ \frac {4 x}{b^{3}}-\frac {x^{3}}{6 b}-\frac {6 \cos \left (b x \right ) \sinIntegral \left (b x \right )}{b^{4}}+\frac {3 x^{2} \cos \left (b x \right ) \sinIntegral \left (b x \right )}{b^{2}}+\frac {3 \sinIntegral \left (2 b x \right )}{b^{4}}-\frac {4 \cos \left (b x \right ) \sin \left (b x \right )}{b^{4}}+\frac {x^{2} \cos \left (b x \right ) \sin \left (b x \right )}{2 b^{2}}-\frac {6 x \sinIntegral \left (b x \right ) \sin \left (b x \right )}{b^{3}}+\frac {x^{3} \sinIntegral \left (b x \right ) \sin \left (b x \right )}{b}-\frac {2 x \left (\sin ^{2}\left (b x \right )\right )}{b^{3}} \]
command
integrate(x^3*cos(b*x)*sin_integral(b*x),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {b^{3} x^{3} - 12 \, b x \cos \left (b x\right )^{2} - 18 \, {\left (b^{2} x^{2} - 2\right )} \cos \left (b x\right ) \operatorname {Si}\left (b x\right ) - 12 \, b x - 3 \, {\left ({\left (b^{2} x^{2} - 8\right )} \cos \left (b x\right ) + 2 \, {\left (b^{3} x^{3} - 6 \, b x\right )} \operatorname {Si}\left (b x\right )\right )} \sin \left (b x\right ) - 18 \, \operatorname {Si}\left (2 \, b x\right )}{6 \, b^{4}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (x^{3} \cos \left (b x\right ) \operatorname {Si}\left (b x\right ), x\right ) \]