# Integral of [sinx * sin(x^2)]

1. Dec 25, 2012

I've never cracked this 1 yet, and I don't remember if it's domain was [0,1] or [0,∞), pretty sure it was 1 of the 2, and not anything with -∞ or ∏/2 for example

∫[sinx * sin(x^2)]dx

2. Dec 25, 2012

### Simon Bridge

3. Dec 25, 2012

### lurflurf

sin(x)* sin(x^2)=[sin((x-1/2)^2)-sin((x+1/2)^2)]sin(1/4)/2+[cos((x-1/2)^2)-cos((x+1/2)^2)]cos(1/4)/2

Your integral is then easily expressed in terms ofFresnel integrals. As far as what limits make the answer tidy, probably none.