BackIntegration by Parts definitions
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1/15BackSkip to main contentBackIntegration by Parts
A method for integrating products of functions when substitution fails, based on reversing the product rule for derivatives. Product Rule
A differentiation rule for finding the derivative of a product of two functions, foundational for deriving integration by parts. u-Substitution
A technique for simplifying integrals by substituting part of the integrand with a new variable, often ineffective for products. Definite Integral
An integral evaluated over specific bounds, requiring application of limits to all terms after integration by parts. Indefinite Integral
An integral without bounds, resulting in a general antiderivative plus a constant of integration. Tabular Method
An organized approach using a table of derivatives and integrals to streamline repeated integration by parts. LIATE
A mnemonic for choosing u in integration by parts: Logarithmic, Inverse, Algebraic, Trigonometric, Exponential. Constant of Integration
An arbitrary constant added to indefinite integrals, omitted in definite integrals. Derivative
A measure of how a function changes as its input changes, used in the product rule and integration by parts. Antiderivative
A function whose derivative is the given function, found through integration. Bounds
The upper and lower limits of integration, applied to all terms in definite integrals. Integrand
The function being integrated, often a product of two functions in integration by parts. Repeated Integration by Parts
A process where integration by parts is applied multiple times to fully evaluate an integral. Power Rule
A rule for differentiating or integrating powers of x, often used when finding derivatives in integration by parts. Variable Substitution
A method for simplifying integrals by changing variables, distinct from integration by parts.
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