111.33 Problem number 44

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

Optimal antiderivative \[ -\frac {5 x}{4 b^{2}}+\frac {2 \cos \left (b x \right ) \sinIntegral \left (b x \right )}{b^{3}}-\frac {x^{2} \cos \left (b x \right ) \sinIntegral \left (b x \right )}{b}-\frac {\sinIntegral \left (2 b x \right )}{b^{3}}+\frac {5 \cos \left (b x \right ) \sin \left (b x \right )}{4 b^{3}}+\frac {2 x \sinIntegral \left (b x \right ) \sin \left (b x \right )}{b^{2}}+\frac {x \left (\sin ^{2}\left (b x \right )\right )}{2 b^{2}} \]

command

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

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

\[ -\frac {2 \, b x \cos \left (b x\right )^{2} + 4 \, {\left (b^{2} x^{2} - 2\right )} \cos \left (b x\right ) \operatorname {Si}\left (b x\right ) + 3 \, b x - {\left (8 \, b x \operatorname {Si}\left (b x\right ) + 5 \, \cos \left (b x\right )\right )} \sin \left (b x\right ) + 4 \, \operatorname {Si}\left (2 \, b x\right )}{4 \, b^{3}} \]

Fricas 1.3.7 via sagemath 9.3 output

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