# How do you find the integral #int_1^2e^(1/x)/x^2dx# ?

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To find the integral ∫_1^2 e^(1/x)/x^2 dx, we can use the substitution method. Let u = 1/x, then du = -1/x^2 dx. This gives us du = -dx/x^2.

Now, we need to change the limits of integration accordingly. When x = 1, u = 1/1 = 1, and when x = 2, u = 1/2.

Next, we substitute u = 1/x and du = -dx/x^2 into the integral:

∫_1^2 e^(1/x)/x^2 dx = ∫_1^2 e^u du

Now, integrating e^u with respect to u:

= e^u + C

Now, we evaluate the integral from u = 1 to u = 1/2:

= e^(1/2) - e^1

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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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