What is the indefinite integral of e^(1/x)/x^2?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the indefinite integral of e^(1/x)/x^2

`int` e^(1/x)/x^2 dx

let 1/x = y, dy/dx = -1/x^2

=> - `int` e^(y) dy

=> - ` ` e^(y)

substitute y = 1/x

=> -e^(1/x)

The required integral is -e^(1/x) + C

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll use the substitution method to solve the indefinite integral.

Let 1/x = t.

We'll differentiate both sides;

-dx/x^2 = dt => dx/x^2 = -dt

`int`[e^(1/x)]dx/x^2 = - `int` (e^t)dt

`int` - ` ` (e^t)dt = - e^t + C

The requested indefinite integral of the function is `int`[e^(1/x)]dx/x^2 = -e^(1/x) + C.

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