Pure · Integration
Chapter 1 · 4
The idea
Integrating with partial fractions
Splitting a rational function into partial fractions so each piece integrates to a logarithm — turning an impossible-looking fraction into a sum of ln terms.
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Pure · Integration
Integrating with partial fractions
Splitting a rational function into partial fractions so each piece integrates to a logarithm — turning an impossible-looking fraction into a sum of ln terms.
Why it works
Split, then integrate
A fraction like has no standard integral as it stands — the bottom isn't the derivative of anything tidy, so the reverse chain rule won't bite. But you already know how to break such a fraction into partial fractions, and each piece is something you can integrate. That fraction is the lesson's running example; by the worked examples it will be two logs.Each piece is a log
The key fact is that a single partial fraction integrates straight to a logarithm:Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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