Evaluate the limit limit gose from x to 4 (x/x-4)integral from x to 4

If you mean

∫[x,4] x/(x-4) dx

that's a bit unusual to have the variable of integration as one of the limits. But ok, let's work it out as-is.

∫x/(x-4) dx = x + 4 log(x-4)

Evaluating that at 4 and x, we have

(4+4log(0))-(x+4log(x-4))

Looks like -∞ to me. That upper limit of 4 is a killer