Integrate cos(x^2) from 0 to infinity

What if [tex] x'a' [/tex] (x is increased to any power like? [tex] int_ and {3} or you can expand the [tex]-cos (x-{2})[/tex] into a series and then integrate each term (and get an approximation). By the way, how can you prove this: [tex] ,int_{0} ,infty (x{2}) dx = int_{0} ,sin sin sin(x{2}) dx = frac{1} {2}sqrt frac {2} [/tex] though not so ... ................
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