# How do you evaluate the integral #int sqrt(2x+3)dx#?

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To evaluate the integral ∫√(2x+3)dx, we use a u-substitution. Let u = 2x + 3. Then, du/dx = 2, and dx = du/2. Substituting these into the integral, we get:

∫√(2x+3)dx = ∫√u * (du/2) = (1/2)∫√u du

Now, we integrate √u with respect to u:

(1/2)∫√u du = (1/2) * (2/3) * u^(3/2) + C = (1/3)u^(3/2) + C

Finally, substituting back u = 2x + 3, we get the result:

(1/3)(2x + 3)^(3/2) + 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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