# How do you evaluate the indefinite integral #int (4x^5-6x^3+7x^2-8)dx#?

The above answer uses the formula:

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To evaluate the indefinite integral (\int (4x^5 - 6x^3 + 7x^2 - 8) , dx), you would apply the power rule for integration.

The indefinite integral of (x^n) with respect to (x) is (\frac{1}{n+1}x^{n+1} + C), where (C) is the constant of integration.

Using this rule for each term in the expression, you would get:

(\int 4x^5 , dx = \frac{4}{6}x^6 + C = \frac{2}{3}x^6 + C)

(\int -6x^3 , dx = -\frac{6}{4}x^4 + C = -\frac{3}{2}x^4 + C)

(\int 7x^2 , dx = \frac{7}{3}x^3 + C)

(\int -8 , dx = -8x + C)

So, putting it all together, the indefinite integral is:

(\frac{2}{3}x^6 - \frac{3}{2}x^4 + \frac{7}{3}x^3 - 8x + 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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