Miss Battaglia AP Calculus 8-2 Integration by Parts Objective: Find an antiderivative using integration by parts. Miss Battaglia AP Calculus

Integration by Parts If u and v are functions of x and have continuous derivatives, then

Logs Inverse Trig Algebraic Trig Exponential LIATE Logs Inverse Trig Algebraic Trig Exponential

Derived from…

Guidelines for Integration by Parts Try letting dv be the most complicated portion of the integrand that fits a basic integration rule. Then u will be the remaining factor(s) of the integrand. Try letting u be the portion of the integrand whose derivative is a function simpler than u. Then dv will be the remaining factor(s) of the integrand. Note that dv always includes the dx of the original integrand.

Integration by Parts Find

Integration by Parts Find

An Integrand with a Single Term Find

Repeated Use of Integration by Parts Find

Integration by Parts Find

Summary of Common Integrals Using Integration by Parts 1. For integrals of the form let u = xn and let dv = eaxdx, sin ax dx, or cos ax dx 2. For integrals of the form let u = lnx, arcsin ax, or arctan ax and let dv = xnd 3. For the integrals of the form let u = sin bx or cos bx and let dv = eaxdx

Classwork/ Homework Read 8.2 Page 533 #11, 13, 15, 19, 27, 29, 32, 83, 99