# How do you evaluate the integral #int e^sqrtx#?

Substitute:

we have:

we can now integrate by parts:

undoing the substitution:

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Please see below for an alternative solution.

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To evaluate the integral ∫e^√x, you can use a substitution method. Let u = √x, then du = (1/(2√x))dx. Rearranging gives dx = 2u du. Substituting these into the integral yields ∫2ue^u du. Integrating by parts or using tabulated integrals, the result is 2(e^√x - √x e^√x) + C, where C is the constant of integration.

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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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