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