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The denominator of the integrand factors as
x2 + 5x + 6 = (x + 2)(x + 3).
Using the partial fractions technique, we find that
Now we can use the FTC.
The denominator factors as
-3x2 – x + 4 = (3x + 4)(-x + 1).
Using partial fractions, we find that
Now we use the FTC:
2x2 + 3x + 1 = (2x + 1)(x + 1).
Using partial fractions we find that
This means that