# How do you find the integral of #(6x+1)/(x^2+2x+3)#?

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To find the integral of (\frac{{6x+1}}{{x^2+2x+3}}), you can use partial fraction decomposition. First, complete the square in the denominator to rewrite it as (x^2+2x+3 = (x+1)^2 + 2). Then, rewrite the integral using partial fractions, solve for the constants, and integrate each term separately. The result will be:

[ \int \frac{{6x+1}}{{x^2+2x+3}} dx = \int \left( \frac{Ax + B}{{(x+1)^2 + 2}} + \frac{Cx + D}{{(x+1)^2 + 2}} \right) dx ]

where (A), (B), (C), and (D) are constants to be determined. After finding the constants, integrate each term separately to get 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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