8-2 Integration by Parts(Day 2)

Objective: Find an antiderivative using integration by parts.

Miss BattagliaAP Calculus

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

Integration by Parts

LogsInverse TrigAlgebraicTrigExponential

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Derived from…

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 dbv will be the remaining factor(s) of the integrand.

Note that dv always includes the dx of the original integrand.

Guidelines for Integration by Parts

Find

Integration by Parts

Find

Integration by Parts

Find

An Integrand with a Single Term

Find

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

Summary of Common Integrals Using Integration by Parts

Page 533 #33, 35, 37, 42, 55, 61, 63, 67, 119

Classwork/ Homework