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