Calculus › Section I · Integration techniques and improper integrals › Topic I.5
Partial fractions
Adding fractions glues simple pieces into one complicated fraction; partial fractions runs that process backwards. It is a purely algebraic step, but it unlocks the calculus: each simple piece integrates to a logarithm or an arctangent, while the combined form resists everything.
In this topic
- Adding fractions, run backwards
- The setup: one term per factor
- Worked example: distinct linear factors
- When long division comes first
- Worked example: a repeated factor
- Worked example: an irreducible quadratic
- Applied: finishing separable equations
- Common mistakes to avoid
- Key takeaways
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Standards: 6 (BC)