Integration by Parts
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Understanding the Technique
Integration by Parts is a powerful technique derived from the product rule for derivatives. This method allows us to integrate the product of two functions. The formula is as follows:
∫ u dv = uv - ∫ v du
Where u and dv are chosen parts of the integrand.
Choosing u and dv
Typically, you choose u to be a function that becomes simpler when differentiated, and dv to be a function that you can easily integrate. A handy mnemonic for choosing u is LIATE:
- Logarithmic
- Inverse trigonometric
- Algebraic
- Trigonometric
- Exponential