Optimal antiderivative \[ -\frac {8 \cos \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{5 b^{5} \pi ^{3}}+\frac {x^{4} \cos \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{5 b \pi }+\frac {x^{5} \mathrm {S}\left (b x \right )}{5}-\frac {4 x^{2} \sin \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{5 b^{3} \pi ^{2}} \]
command
integrate(x^4*fresnel_sin(b*x),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {\pi ^{3} b^{5} x^{5} \operatorname {S}\left (b x\right ) - 4 \, \pi b^{2} x^{2} \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) + {\left (\pi ^{2} b^{4} x^{4} - 8\right )} \cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )}{5 \, \pi ^{3} b^{5}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (x^{4} {\rm fresnels}\left (b x\right ), x\right ) \]