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This integration technique is particularly useful whenever either a sum-of-square or a difference-of-squares is found within the integrand. This approach is typically implemented to help reduce the complexity found among square-root functions.
| Difference of Squares | ||
| Substitution | Expression | Protocols |
| Sine | \(\sqrt{a^2-u^2}\) | \(u=a\,\texttt{sin}(\theta)\) |
| Secant | \(\sqrt{u^2-a^2}\) | \(u=a\,\texttt{sec}(\theta)\) |
| Sum of Squares | ||
| Substitution | Expression | Protocols |
| Tangent | \(\sqrt{a^2+u^2}\) | \(u=a\,\texttt{tan}(\theta)\) |
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