# How do you find the indefinite integral of #int (-24x^5-10x) dx#?

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To find the indefinite integral of ( \int (-24x^5 - 10x) , dx ):

- Use the power rule for integration.
- Add 1 to the exponent and divide by the new exponent.
- Apply the constant multiple rule for integration.

The result is: [ -\frac{24}{6}x^6 - \frac{10}{2}x^2 + C ]

Simplify to obtain the final result: [ -4x^6 - 5x^2 + C ]

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To find the indefinite integral of ( \int (-24x^5 - 10x) , dx ), you can use the power rule for integration. This rule states that for a term of the form ( ax^n ), where ( a ) is a constant and ( n ) is any real number except for -1, the indefinite integral is given by ( \frac{a}{n+1}x^{n+1} + C ), where ( C ) is the constant of integration.

Applying this rule to each term separately:

For ( -24x^5 ), the integral becomes ( \frac{-24}{5+1}x^{5+1} = -4x^6 ).

For ( -10x ), the integral becomes ( \frac{-10}{1+1}x^{1+1} = -5x^2 ).

Adding these two results together, the indefinite integral of ( \int (-24x^5 - 10x) , dx ) is ( -4x^6 - 5x^2 + 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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