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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 \(\sqrt{a^2+u^2}\) \(u=a\,\texttt{tan}(\theta)\)
* Note: The presence of the square-root function is not required to implement these techniques. 

Integration

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