Optimal antiderivative \[ \frac {x \cos \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{2 b \pi }-\frac {\FresnelC \left (b x \right )}{2 b^{2} \pi }+\frac {x^{2} \mathrm {S}\left (b x \right )}{2} \]
command
integrate(x*fresnel_sin(b*x),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {\pi b^{3} x^{2} \operatorname {S}\left (b x\right ) + b^{2} x \cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) - \sqrt {b^{2}} \operatorname {C}\left (\sqrt {b^{2}} x\right )}{2 \, \pi b^{3}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (x {\rm fresnels}\left (b x\right ), x\right ) \]