\[ \int x^2 \text {Si}(a+b x)^2 \, dx \]
Optimal antiderivative \[ \frac {2 x}{3 b^{2}}+\frac {a \cosineIntegral \left (2 b x +2 a \right )}{b^{3}}-\frac {a \cos \left (2 b x +2 a \right )}{3 b^{3}}+\frac {x \cos \left (2 b x +2 a \right )}{6 b^{2}}-\frac {a \ln \left (b x +a \right )}{b^{3}}-\frac {4 \cos \left (b x +a \right ) \sinIntegral \left (b x +a \right )}{3 b^{3}}+\frac {2 a^{2} \cos \left (b x +a \right ) \sinIntegral \left (b x +a \right )}{3 b^{3}}-\frac {2 a x \cos \left (b x +a \right ) \sinIntegral \left (b x +a \right )}{3 b^{2}}+\frac {2 x^{2} \cos \left (b x +a \right ) \sinIntegral \left (b x +a \right )}{3 b}+\frac {a^{2} \left (b x +a \right ) \sinIntegral \left (b x +a \right )^{2}}{3 b^{3}}-\frac {a x \left (b x +a \right ) \sinIntegral \left (b x +a \right )^{2}}{3 b^{2}}+\frac {x^{2} \left (b x +a \right ) \sinIntegral \left (b x +a \right )^{2}}{3 b}+\frac {2 \sinIntegral \left (2 b x +2 a \right )}{3 b^{3}}-\frac {a^{2} \sinIntegral \left (2 b x +2 a \right )}{b^{3}}-\frac {2 \cos \left (b x +a \right ) \sin \left (b x +a \right )}{3 b^{3}}+\frac {2 a \sinIntegral \left (b x +a \right ) \sin \left (b x +a \right )}{3 b^{3}}-\frac {4 x \sinIntegral \left (b x +a \right ) \sin \left (b x +a \right )}{3 b^{2}}-\frac {\sin \left (2 b x +2 a \right )}{12 b^{3}} \]
command
integrate(x^2*sin_integral(b*x+a)^2,x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\left (b x - 2 \, a\right )} \cos \left (b x + a\right )^{2} + 4 \, {\left (b^{2} x^{2} - a b x + a^{2} - 2\right )} \cos \left (b x + a\right ) \operatorname {Si}\left (b x + a\right ) + 2 \, {\left (b^{3} x^{3} + a^{3}\right )} \operatorname {Si}\left (b x + a\right )^{2} + 3 \, b x + 3 \, a \operatorname {Ci}\left (2 \, b x + 2 \, a\right ) + 3 \, a \operatorname {Ci}\left (-2 \, b x - 2 \, a\right ) - 6 \, a \log \left (b x + a\right ) - {\left (4 \, {\left (2 \, b x - a\right )} \operatorname {Si}\left (b x + a\right ) + 5 \, \cos \left (b x + a\right )\right )} \sin \left (b x + a\right ) - 2 \, {\left (3 \, a^{2} - 2\right )} \operatorname {Si}\left (2 \, b x + 2 \, a\right )}{6 \, b^{3}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (x^{2} \operatorname {Si}\left (b x + a\right )^{2}, x\right ) \]