# How do you integrate #inte^(1/x)/x^2# using substitution?

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and undoing the substitution:

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To integrate ( \frac{e^{1/x}}{x^2} ) using substitution, let ( u = \frac{1}{x} ). Then ( du = -\frac{1}{x^2}dx ).

Substitute ( u ) and ( du ) into the integral:

[ \int \frac{e^{1/x}}{x^2} dx = -\int e^u du ]

Now integrate ( -e^u ):

[ -\int e^u du = -e^u + C ]

Finally, substitute back ( u = \frac{1}{x} ) to get the final result:

[ \int \frac{e^{1/x}}{x^2} dx = -e^{1/x} + C ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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