# What is the integral of #int x^3/(1+x^2)dx#?

The answer is

Perform the substitution

Therefore,

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The integral of ( \int \frac{x^3}{1+x^2} , dx ) can be solved using the method of partial fractions. After decomposing the fraction into simpler terms, the integral can be expressed as ( \frac{1}{2} \ln|1+x^2| + \frac{1}{2}x \arctan(x) + 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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