\[ \int \text {CosIntegral}(a+b x) \, dx \]
Optimal antiderivative \[ \frac {\left (b x +a \right ) \cosineIntegral \left (b x +a \right )}{b}-\frac {\sin \left (b x +a \right )}{b} \]
command
integrate(fresnel_cos(b*x+a),x, algorithm="maxima")
Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output
\[ \frac {{\left (b x + a\right )} \operatorname {C}\left (b x + a\right ) - \frac {\sin \left (\frac {1}{2} \, \pi b^{2} x^{2} + \pi a b x + \frac {1}{2} \, \pi a^{2}\right )}{\pi }}{b} \]
Maxima 5.44 via sagemath 9.3 output
\[ \int {\rm Ci}\left (b x + a\right )\,{d x} \]________________________________________________________________________________________