# How do you integrate #(2x) / (4x^2 + 12x + 9)# using partial fractions?

You don't use partial fractions, because the denominator is a perfect square.

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To integrate ( \frac{2x}{4x^2 + 12x + 9} ) using partial fractions, follow these steps:

- Factor the denominator ( 4x^2 + 12x + 9 ) into its irreducible quadratic factors.
- Write the fraction ( \frac{2x}{4x^2 + 12x + 9} ) as a sum of partial fractions, where the numerator of each fraction is a constant or a linear polynomial, and the denominator is one of the irreducible quadratic factors.
- Solve for the unknown coefficients by equating the original fraction to the sum of the partial fractions.
- Once you have found the partial fraction decomposition, integrate each term separately.
- Combine the integrals of the partial fractions to obtain the final result.

For detailed step-by-step instructions on how to perform partial fraction decomposition and integrate each term, you can refer to calculus textbooks or online resources covering the topic of partial fractions.

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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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