Main Question or Discussion Point
If so, could it be used to integrate sin(x)/ln(x)
That was the second part of the question, I believe he was more looking for the first part... (And if you believe substituting a function with a fourier series in order to integrate it is easy, then you must be a genius...)You aren't going to find a simple antiderivative of that and if you are looking for a definite integral just use a numerical method directly on the integral.
Not exactly. It has to be periodic. But if you just want a Fourier series that works over an interval, just take that interval and look at that, and then take infinitely many copies of the function on that interval and it's periodic.Anyways, doesn't a function have to be oscillating to have a fourier series?