A-level Mathematics/MEI/C3/Integration

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Integration by Substitution[edit]

Integration by Parts[edit]

Integration by parts is used when you have two functions multiplied together, such as ln x and a simple polynomial, where 1 function is not the derivative of the other. As an example:

In this expression use the substitutions: and . In almost all other expressions, the polynomial is taken as u. After substituting, the expression in the example becomes:

After integrating and differentiating the respective parts of the expression, this becomes: