CALCULUS Understanding Its Concepts and Methods

Integration by parts

Integration by parts is a method for
integrating the product of two functions
*f*(*x*)
and
*g*(*x*).
First find
*G*(*x*)
so that
*G'*(*x*) = *g*(*x*).
Then apply the
formula

The functions
*f*
and
*g*
are the two parts. The part
*f*
is differentiated, the part
*g*
is integrated.

Sometimes the formula is written

where
*u* = *f*(*x*)
and
*v* = *G*(*x*),
so
*du* =
*f'*(*x*)* dx*
and
*dv* = *g*(*x*)* dx*.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.