When integrating functions involving polynomials in the denominator, partial fractions can be used to simplify integration. New students of calculus will find it handy to learn how to decompose functions into partial fractions not just for integration, but for more advanced studies as well.

A proper fraction has a larger power in the denominator than in the numerator. If the power of the numerator is larger than or equal to the power of the denominator, it is improper and must be divided using long division

This solves forGenerally, we multiply by the factor and plug in the value of the root. That solves for the coefficient of the fraction whose denominator has that factor.

Notice that the term within it goes to 0, butdoesn't. Furthermore, multiplying everything by that factor makes sure that we don't get any division by 0 problems.

Although the u-subs are very easy to do, it is still recommended that you show all your work if you are not familiar with doing these types of integrals yet.

Because both sides are equal, that means that the coefficients of theterms are equal. We obtain a system of equations, where the number of equations depends on the degree of the denominator that you started out with.

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