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@jemoka / Jemoka Knowledge Base / wiki/concepts/integrating_factor.md
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--- title: "integrating factor" type: concept related: [Integrating Factor] source: https://www.jemoka.com/posts/kbhintegrating_factor/ confidence: high status: active --- The integrating factor \(\rho(x)\) is a value that helps undo the product rule. For which: \begin{equation} log(\rho(x)) = \int P(x)dx \end{equation} for some function \(P(x)\). Separating the \(\rho(x)\) out, we have therefore: \begin{equation} e^{\int P dx} = \rho(x) \end{equation} Why is this helpful and undoes the product rule? This is because of a very interesting property of how \(\rho(x)\) behaves.