# How do you use substitution to integrate #(2x+7)/(x^2+5x+6) dx#?

The answer can be written as

You don't need substitution to do this integral. Use the Method of Partial Fractions instead.

Now substitute, integrate, and use properties of logarithms:

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To integrate the given rational function using substitution, you can first decompose the denominator into linear factors, then proceed with a partial fraction decomposition. This involves expressing the rational function as a sum of simpler fractions. Once you have the partial fraction decomposition, you can integrate each term individually. After integrating, you can then substitute back to obtain 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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