# What is #int g(x) = (5-6x^3) / x dx#?

Umm, you kinda mixed up the notation there buddy.

Whereas

I'm guessing you mean the first one, which the way you wrote isn't technically wrong but it's a bit confusing. In that case, we have

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The integral of g(x) = (5 - 6x^3) / x with respect to x is:

∫ g(x) dx = ∫ (5/x - 6x^2) dx

Using the rules of integration:

∫ (5/x - 6x^2) dx = 5∫(1/x) dx - 6∫(x^2) dx

Integrating each term separately:

∫(1/x) dx = ln|x| + C1 (where C1 is the constant of integration) ∫(x^2) dx = (1/3)x^3 + C2 (where C2 is the constant of integration)

Therefore, the integral of g(x) is:

5ln|x| - 2x^3 + C, where C = C1 + C2 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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