111.12 Problem number 16

\[ \int \frac {\text {Si}(b x)^2}{x^3} \, dx \]

Optimal antiderivative \[ \mathit {CannotIntegrate} \left (\frac {\sinIntegral \left (b x \right )^{2}}{x^{3}}, x\right ) \]

command

integrate(sin_integral(b*x)^2/x^3,x, algorithm="fricas")

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

\[ \frac {2 \, b^{2} x^{2} \operatorname {Ci}\left (2 \, b x\right ) + 2 \, b^{2} x^{2} \operatorname {Ci}\left (-2 \, b x\right ) - 2 \, b x \cos \left (b x\right ) \operatorname {Si}\left (b x\right ) - {\left (b^{2} x^{2} + 2\right )} \operatorname {Si}\left (b x\right )^{2} + \cos \left (b x\right )^{2} - 2 \, {\left (2 \, b x \cos \left (b x\right ) + \operatorname {Si}\left (b x\right )\right )} \sin \left (b x\right ) - 1}{4 \, x^{2}} \]

Fricas 1.3.7 via sagemath 9.3 output

\[ {\rm integral}\left (\frac {\operatorname {Si}\left (b x\right )^{2}}{x^{3}}, x\right ) \]