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Integrate.

Answer

The denominator of the integrand factors as

x^{2} + 5x + 6 = (x + 2)(x + 3).

Using the partial fractions technique, we find that

This means

Now we can use the FTC.

The denominator factors as

-3x^{2} – x + 4 = (3x + 4)(-x + 1).

Using partial fractions, we find that

Now we use the FTC:

2x^{2} + 3x + 1 = (2x + 1)(x + 1).

Using partial fractions we find that

This means that