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Polynomial + Trig or Exponential Special Case (Table Method)

Principles

Used to evaluate Integration By Parts (IBP) polynomials where u = polynomial and dv = trig or exponential
Set up the special case table and multiply the item in the u column by the dv to the bottom right of it
Alternate between positive and negative
Keep adding into equation before for values where the derivative of u > 0

Table

For $\int{x^2e^{2x}dx}$

u (d)	dv (anti-d)
$x^2$	$e^{2x}$
2x	$\frac12e^{2x}$
2	$\frac14e^{2x}$
0	$\frac18e^{2x}$

Anki

START Cloze The {Table Method::method} is used for cases where u and dv are {polynomial and trig/exponential::type of thing}. The grouped terms should alternate between {positive and negative::sign changes} Back: DECK: IntegralCalculus Tags: IBP

END

Practice

!Section C Part I

References:

John Mavrick's Garden

Polynomial + Trig or Exponential Special Case (Table Method)

Principles

Table

Anki

Practice

Backlinks

Interactive Graph