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I tried that one and also sin(x^b).
What sorts did you try? I tried something of the form ln(bsinx2) or similar, in the hope that I could cancel the trig term, but it did not work. Maybe trying to use a trig identity would fare better?
Hmm. So, there might not be a way. I will still try to look for one however. It seems I never get to use this little tool.
Those are not Fresnel integrals so he made one of two mistakes. He did not put the square in the proper spot or he does not know what a Fresnel Integral is.
But that is not a Fresnel integral. They said that the middle row contains two Fresnel integrals... so either they meant that it does not contain two Fresnel integrals, or they didn't parenthesise the powers properly...
If you meant the examples at the end of that pdf then it meant
and not the integral you want.
I know you can do it without DUIS (e.g. gamma function method), but was curious if it was made really simple via DUIS (like integrating sinx/x).
The last page here says you can do it.
I've been trying to do
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?