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