How Do You Solve Integration by Parts for ∫ x*(ln(x))^4 dx?

[fallen186]

Homework Statement

$$\int x*(ln(x))^4dx = 4ln|x|^3-12ln|x|$$

Homework Equations

The Attempt at a Solution

I did chart method
u...dv...+/-
------------------------
x...ln|x|^4...+
1...(4ln|x|^3)/x.. -
0...12ln|x|...+
......-

 

[Mark44]

What's the question?
What's the significance of your chart? Is u = x? And is dv = (ln|x|)^4 *dx? If so, this is not at all a useful substitution.

 

[Gib Z]

The chart is the authors attempt at a Tabular Integration by Parts: http://en.wikipedia.org/wiki/Integration_by_parts#Tabular_integration_by_parts

Hes probably asking us just to check his work.

To fallen186 - When we do Tabular integration, the Column with our chosen "u" is the derivatives column, whilst the "dv" column are for the integrals, not for derivatives again. And as Mark44 said, its probably better if you reconsider your substitutions.

 

[workerant]

I was taught this about picking the correct substitution:

HIGHEST priority for choice of u (i.e. make these things "u")
lnx logx arctanx and things like that LEVEL 1
x^2 (i.e. polynomials) or things like that LEVEL 2
cos x sin x LEVEL 3
e^x LEVEL 4
LOWEST priority of choice of u.


Have you done such?

Also, many textbooks include reduction formulas in the back and sometimes test just to see if you are familiar with such formulas. This may be the case here as well, although using integration by parts is not at all difficult in this problem.

 

[Gib Z]

Yes I have, the algorithim for picking the substitution is often shortened to "ILATE" or "LIATE". I learned ILATE but it doesn't really matter unless you have some nasty product of both an Inverse Trig and a log.

Basically were saying, fallen186, you should pick your log term as your u sub.