# How do you find the indefinite integral of #int (4x^-5) dx#?

Thus

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To find the indefinite integral of ∫(4x^(-5)) dx, you can use the power rule for integration:

∫x^n dx = (x^(n+1))/(n+1) + C

Applying this rule to the given function:

∫(4x^(-5)) dx = (4x^(-5+1))/(-5+1) + C = (4x^(-4))/(-4) + C = - (1/4) * (1/x^4) + C = - (1/4x^4) + C

So, the indefinite integral of ∫(4x^(-5)) dx is - (1/4x^4) + C, where C is the constant of integration.

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To find the indefinite integral of ( \int 4x^{-5} , dx ):

- Apply the power rule of integration, which states that ( \int x^n , dx = \frac{1}{n+1} x^{n+1} + C ), where ( C ) is the constant of integration.
- Apply the power rule to the given integral: ( \int 4x^{-5} , dx = \frac{4}{-5+1} x^{-5+1} + C ).
- Simplify the expression: ( \int 4x^{-5} , dx = -\frac{4}{4} x^{-4} + C ).
- Further simplify to get the final result: ( \int 4x^{-5} , dx = -x^{-4} + 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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