\[ \int \cos (b x) \text {Si}(b x) \, dx \]
Optimal antiderivative \[ \frac {\cosineIntegral \left (2 b x \right )}{2 b}-\frac {\ln \left (x \right )}{2 b}+\frac {\sinIntegral \left (b x \right ) \sin \left (b x \right )}{b} \]
command
integrate(cos(b*x)*sin_integral(b*x),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {4 \, \sin \left (b x\right ) \operatorname {Si}\left (b x\right ) + \operatorname {Ci}\left (2 \, b x\right ) + \operatorname {Ci}\left (-2 \, b x\right ) - 2 \, \log \left (x\right )}{4 \, b} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\cos \left (b x\right ) \operatorname {Si}\left (b x\right ), x\right ) \]