# How do you find the antiderivative of #(x^(3) + 2x)/(x^(4) + 4x^(2) +2)#?

Here,

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To find the antiderivative of (\frac{x^3 + 2x}{x^4 + 4x^2 + 2}), perform polynomial long division to rewrite the expression as (Q(x) + \frac{R(x)}{x^4 + 4x^2 + 2}). Then, integrate each term separately. The resulting antiderivative will be a combination of logarithmic and arctangent functions.

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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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