\[ \int x \text {Si}(b x) \, dx \]
Optimal antiderivative \[ \frac {x \cos \left (b x \right )}{2 b}+\frac {x^{2} \sinIntegral \left (b x \right )}{2}-\frac {\sin \left (b x \right )}{2 b^{2}} \]
command
integrate(x*sin_integral(b*x),x, algorithm="maxima")
Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output
\[ \frac {1}{2} \, x^{2} \operatorname {Si}\left (b x\right ) + \frac {b x \cos \left (b x\right ) - \sin \left (b x\right )}{2 \, b^{2}} \]
Maxima 5.44 via sagemath 9.3 output
\[ \int x {\rm Si}\left (b x\right )\,{d x} \]________________________________________________________________________________________