# What is the antiderivative of # (x+1)(2x-1)#?

Finding the integral of a function is equivalent to finding its antiderivative.

We apply the power rule to find this.

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where

We start with:

We multiply the two binomials:

We break up the integral into three separate integrals:

Now we integrate:

Simplifying:

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The antiderivative of (x+1)(2x-1) is ( \frac{1}{3}x^3 + \frac{1}{2}x^2 - 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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