What is the integral of sin(pi(x^2))?

Question

With steps if possible too please!

Answer 1

[S(square root(2)*x)]/[square root(2)]

S(x): Fresnel S[x]: Fresnel integral [properties]

another possible way of writing it
[FresnelS{square root(2)}{x}]/[square root(2)]

Good Luck. If you need more help let me know.

Answer 2

So sorry, but this integral cannot be expressed
in terms of elementary functions. It is a
type of Fresnel integral.
Look up Fresnel integrals on Wikipedia
for more information.