# How do you evaluate the integral #int dx/(x+1)^3#?

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To evaluate the integral ( \int \frac{dx}{(x+1)^3} ), you can use the method of integration by partial fractions. Here are the steps:

- Express the integrand as a sum of partial fractions.
- Determine the constants in the partial fraction decomposition.
- Integrate each term separately.

For ( \int \frac{dx}{(x+1)^3} ), the partial fraction decomposition is:

[ \frac{1}{(x+1)^3} = \frac{A}{x+1} + \frac{B}{(x+1)^2} + \frac{C}{(x+1)^3} ]

Where ( A ), ( B ), and ( C ) are constants to be determined.

After finding the values of ( A ), ( B ), and ( C ), integrate each term separately. The final result will be the sum of the integrals of each partial fraction term.

This process will give you the solution for the integral ( \int \frac{dx}{(x+1)^3} ).

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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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