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