Evaluate the integral of e^(1/x) / x^2 from [1,2].

Question

I let u =1/x, but then I am stuck because I am not sure what is the derivative of 1/x is?

The answer in the book is e- sqrt(e)

Answer 1

let u=1/x
du = -1/x^2 dx

∫e^(1/x)/x^2 dx
= -∫e^u du
= -e^u = -e^(1/x) [1,2]
= -e^(1/2) + e^(1/1)
...