Question

How do you evaluate the integral `int e^(1/x)/x^2`?

Answer 1

`int e^(1/x)/x^2dx = -e^(1/x) + C`

Explanation:

Substitute: `t=1/x`, `dt = -1/x^2dx`

so we have:

`int e^(1/x)/x^2dx = -int e^tdt = -e^t + C`

and undoing the substitution:

`int e^(1/x)/x^2dx = -e^(1/x) + C`