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