111.6 Problem number 7

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

Optimal antiderivative \[ b \cosineIntegral \left (b x \right )-\frac {\sinIntegral \left (b x \right )}{x}-\frac {\sin \left (b x \right )}{x} \]

command

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

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

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

Fricas 1.3.7 via sagemath 9.3 output

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