\[ \int \text {CosIntegral}(b x) \, dx \]
Optimal antiderivative \[ x \cosineIntegral \! \left (b x \right )-\frac {\sin \! \left (b x \right )}{b} \]
command
integrate(fresnel_cos(b*x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ x \operatorname {Ci}\left (b x\right ) - \frac {\sin \left (b x\right )}{b} \]