Integration by PartsChapter 8 Section 2P. 527

DefinitionIntegration by parts is a method for evaluating a difficult integral. When the integral is a product of functions, the integration by parts formula moves the product out of the equation so that integral can be solved easier.Formulaudv= uv -vduCatchy Phrase to remember the integration by parts equation: ultimate virus-viciously destroysuudv= uv -vduLet dv be the most complicated part of the original integrand that fits a basic integration rule (including dx). Then u will be the remaining factors.Let u be a portion of the integrand whose derivative is a function simpler that u. Then dv will be the remaining factors (including dx).Example 1xsin(x)dxExample 2x2lnx dx Example 3x2ex dx Example 4lnx dx Example 5arcsin(x)dx El FinBy: Jenna, Kristine (Jackie) Chen & Dani - (Minus)