what is the third integral of arcsin(tan(lnX))/X^(4/X)

Because sin can only take values between ±1 the values of tan(ln(x)) must lie in this range for the function to be defined.  This makes the function defined only between certain values of x.  See the graphs below:

There are an infinite number of such regions (e^7pi/4 < x < e^9pi/4, for example).

Which is the region of interest?

Alan or Chris, do either of you have any idea how to do this.  I played with it but I really have no idea.  

I have been trying to fathom what Alan is telling me.

This is a graph of y=atan(sin(lnx))

The graph is broken so the domain must be chosen.

Thanks Alan.