111.14 Problem number 19

\[ \int x^2 \text {Si}(a+b x) \, dx \]

Optimal antiderivative \[ -\frac {2 \cos \left (b x +a \right )}{3 b^{3}}+\frac {a^{2} \cos \left (b x +a \right )}{3 b^{3}}-\frac {a x \cos \left (b x +a \right )}{3 b^{2}}+\frac {x^{2} \cos \left (b x +a \right )}{3 b}+\frac {a^{3} \sinIntegral \left (b x +a \right )}{3 b^{3}}+\frac {x^{3} \sinIntegral \left (b x +a \right )}{3}+\frac {a \sin \left (b x +a \right )}{3 b^{3}}-\frac {2 x \sin \left (b x +a \right )}{3 b^{2}} \]

command

integrate(x^2*sin_integral(b*x+a),x, algorithm="fricas")

Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output

\[ \frac {{\left (b^{2} x^{2} - a b x + a^{2} - 2\right )} \cos \left (b x + a\right ) - {\left (2 \, b x - a\right )} \sin \left (b x + a\right ) + {\left (b^{3} x^{3} + a^{3}\right )} \operatorname {Si}\left (b x + a\right )}{3 \, b^{3}} \]

Fricas 1.3.7 via sagemath 9.3 output

\[ {\rm integral}\left (x^{2} \operatorname {Si}\left (b x + a\right ), x\right ) \]