How do I integrate {(((1 - ln x) x ^ x / a) / x ^ 2) dx and verify

I assume that you have typed the wrong and that it should be the integral of f (x) = (1 - ln x) x1/x/x2 instead. This applies to f (x) = (1 - ln x) e (1 / x) ln x/x2. If we now t = (1 / x) ln x, we get dt = ((1 - ln x) / x2) dx, and the integral turns into ∫ et dt = et + C = x1 / x + C.