# How do you integrate #int (2x-5)/(x^2+2x+2)dx#?

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To integrate ( \int \frac{2x - 5}{x^2 + 2x + 2} , dx ), perform partial fraction decomposition first, which yields ( \frac{2x - 5}{x^2 + 2x + 2} = \frac{Ax + B}{x^2 + 2x + 2} ). Solve for ( A ) and ( B ), then integrate each term separately. The result is ( \ln|x^2 + 2x + 2| - 5\sqrt{2} \tan^{-1}\left(\frac{x + 1}{\sqrt{2}}\right) + 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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