Using partial fractions with DISTINCT QUADRATIC FACTORS

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Partial fractions, like u-substitution and integration by parts, is a method of breaking down one complicated fraction into multiple simpler fractions. The reason this is helpful is because the original fraction might not be something you can integrate, but if you break it down into multiple simpler fractions, those simpler fractions might be easier to integrate.

The most important thing to remember about partial fractions, is that you have to start by factoring the denominator. Once you have the denominator completely factored, you'll need to identify whether the factors are distinct linear factors, repeated linear factors, distinct quadratic factors, distinct linear factors, or a mix of those. The way you break down the fraction into its partial fractions decomposition depends on the kind of factors you find in its denominator.

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