111.7 Problem number 8

\[ \int \frac {\text {Si}(b x)}{x^3} \, dx \]

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

command

integrate(sin_integral(b*x)/x^3,x, algorithm="fricas")

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

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

Fricas 1.3.7 via sagemath 9.3 output

\[ {\rm integral}\left (\frac {\operatorname {Si}\left (b x\right )}{x^{3}}, x\right ) \]