27.25 Problem number 66

\[ \int S(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx \]

Optimal antiderivative \[ \frac {\mathrm {S}\left (b x \right )^{2}}{2 b} \]

command

integrate(fresnel_sin(b*x)*sin(1/2*b^2*pi*x^2),x, algorithm="maxima")

Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output

\[ \frac {\operatorname {S}\left (b x\right )^{2}}{2 \, b} \]

Maxima 5.44 via sagemath 9.3 output

\[ \int {\rm fresnels}\left (b x\right ) \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )\,{d x} \]________________________________________________________________________________________