I tried a couple of parametrizations but did not have any luck producing one that gets the known answer.

]]>(I am assuming they meant cos(x^2) and not cos^2x because the latter is not a Fresnel integral and not very difficult.)

If you meant the examples at the end of that pdf then it meant

and not the integral you want.

]]>This page does it without resorting to DUIS.

]]>tinyurl. com /bj99zrg

(remove spaces)

(I am assuming they meant cos(x[sup]2[/sup]) and not cos[sup]2[/sup]x because the latter is not a Fresnel integral and not very difficult.)

]]>I have never seen it done using differentiation under the integral sign.

]]>and

using DUIS, but I can't think of any kind of useful parametrisation that would work. Every time I do, I usually end up with something that *looks* like you can use integration by parts, but that doesn't work. I'm aware the indefinite integral form of these integrals can't be expressed in terms of elementary functions, so I'm hoping I might have more luck with the improper ones. Can anyone show me a useful parametrisation that would work here?

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