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