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