# How do you integrate #(x^3+2x^2-x) / x dx#?

At first we simplify the integrand

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To integrate ((x^3 + 2x^2 - x) / x) with respect to (x), you can first simplify the expression by dividing every term by (x), resulting in (x^2 + 2x - 1). Then, integrate each term separately. The integral of (x^2) is ((1/3)x^3), the integral of (2x) is (x^2), and the integral of (-1) is (-x). So, the integral of the given expression is ((1/3)x^3 + 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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