\[ \int x^2 \cos (a+b x) \text {Si}(a+b x) \, dx \]
Optimal antiderivative \[ \frac {a x}{2 b^{2}}-\frac {x^{2}}{4 b}-\frac {\cosineIntegral \left (2 b x +2 a \right )}{b^{3}}+\frac {a^{2} \cosineIntegral \left (2 b x +2 a \right )}{2 b^{3}}+\frac {\cos \left (2 b x +2 a \right )}{2 b^{3}}+\frac {\ln \left (b x +a \right )}{b^{3}}-\frac {a^{2} \ln \left (b x +a \right )}{2 b^{3}}+\frac {2 x \cos \left (b x +a \right ) \sinIntegral \left (b x +a \right )}{b^{2}}+\frac {a \sinIntegral \left (2 b x +2 a \right )}{b^{3}}-\frac {a \cos \left (b x +a \right ) \sin \left (b x +a \right )}{2 b^{3}}+\frac {x \cos \left (b x +a \right ) \sin \left (b x +a \right )}{2 b^{2}}-\frac {2 \sinIntegral \left (b x +a \right ) \sin \left (b x +a \right )}{b^{3}}+\frac {x^{2} \sinIntegral \left (b x +a \right ) \sin \left (b x +a \right )}{b}-\frac {\sin ^{2}\left (b x +a \right )}{4 b^{3}} \]
command
integrate(x^2*cos(b*x+a)*sin_integral(b*x+a),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {b^{2} x^{2} - 8 \, b x \cos \left (b x + a\right ) \operatorname {Si}\left (b x + a\right ) - 2 \, a b x - 5 \, \cos \left (b x + a\right )^{2} - {\left (a^{2} - 2\right )} \operatorname {Ci}\left (2 \, b x + 2 \, a\right ) - {\left (a^{2} - 2\right )} \operatorname {Ci}\left (-2 \, b x - 2 \, a\right ) + 2 \, {\left (a^{2} - 2\right )} \log \left (b x + a\right ) - 2 \, {\left ({\left (b x - a\right )} \cos \left (b x + a\right ) + 2 \, {\left (b^{2} x^{2} - 2\right )} \operatorname {Si}\left (b x + a\right )\right )} \sin \left (b x + a\right ) - 4 \, a \operatorname {Si}\left (2 \, b x + 2 \, a\right )}{4 \, b^{3}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (x^{2} \cos \left (b x + a\right ) \operatorname {Si}\left (b x + a\right ), x\right ) \]