111.11 Problem number 13

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

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

command

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

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

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

Fricas 1.3.7 via sagemath 9.3 output

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