This is my second post.In my first one I asked about the integration of trig functions which have a domain other than x only.From the answer I concluded that first you have to take the derivative of the domain then multiply the inverse of that derivative with the integral of the trig function,keeping its domain unchanged.

My question is that does it only work if in the domain x has power 1 or it is also valid for higher powers of x and for exponential expressions in the domain.