\[ \int x^m \text {Si}(b x) \, dx \]
Optimal antiderivative \[ \frac {x^{m} \Gamma \left (1+m , -i b x \right ) \left (-i b x \right )^{-m}}{2 b \left (1+m \right )}+\frac {x^{m} \Gamma \left (1+m , i b x \right ) \left (i b x \right )^{-m}}{2 b \left (1+m \right )}+\frac {x^{1+m} \sinIntegral \left (b x \right )}{1+m} \]
command
integrate(x^m*sin_integral(b*x),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, b x x^{m} \operatorname {Si}\left (b x\right ) + \frac {\Gamma \left (m + 1, i \, b x\right )}{\left (i \, b\right )^{m}} + \frac {\Gamma \left (m + 1, -i \, b x\right )}{\left (-i \, b\right )^{m}}}{2 \, {\left (b m + b\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (x^{m} \operatorname {Si}\left (b x\right ), x\right ) \]