\[ \int \text {CosIntegral}(b x) \, dx \]
Optimal antiderivative \[ x \cosineIntegral \left (b x \right )-\frac {\sin \left (b x \right )}{b} \]
command
integrate(fresnel_cos(b*x),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {\pi b x \operatorname {C}\left (b x\right ) - \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )}{\pi b} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\operatorname {Ci}\left (b x\right ), x\right ) \]