# How do you integrate #(x^3)/(1+x^2)#?

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To integrate (\frac{x^3}{1+x^2}), you can use the method of partial fractions. You start by expressing the integrand as a sum of two fractions with undetermined coefficients:

(\frac{x^3}{1+x^2} = \frac{Ax + B}{1+x^2} + \frac{Cx+D}{1+x^2})

After simplifying and solving for the coefficients (A), (B), (C), and (D), you'll have:

(\int \frac{x^3}{1+x^2} dx = \int \frac{Ax + B}{1+x^2} dx + \int \frac{Cx+D}{1+x^2} dx)

Solving these integrals gives the final result.

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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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