Optimal antiderivative \[ -\frac {35 x^{3} \cos \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{8 b^{5} \pi ^{3}}+\frac {x^{7} \cos \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{8 b \pi }-\frac {105 \,\mathrm {S}\left (b x \right )}{8 b^{8} \pi ^{4}}+\frac {x^{8} \mathrm {S}\left (b x \right )}{8}+\frac {105 x \sin \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{8 b^{7} \pi ^{4}}-\frac {7 x^{5} \sin \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{8 b^{3} \pi ^{2}} \]
command
integrate(x^7*fresnel_sin(b*x),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {{\left (\pi ^{3} b^{7} x^{7} - 35 \, \pi b^{3} x^{3}\right )} \cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) + {\left (\pi ^{4} b^{8} x^{8} - 105\right )} \operatorname {S}\left (b x\right ) - 7 \, {\left (\pi ^{2} b^{5} x^{5} - 15 \, b x\right )} \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )}{8 \, \pi ^{4} b^{8}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (x^{7} {\rm fresnels}\left (b x\right ), x\right ) \]