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