Integrate ln(x)/x^4 using Integration by Parts | Homework Help

Click For Summary

Homework Help Overview

The problem involves integrating the function \(\int{\frac{\ln x}{x^4}dx}\), which falls under the subject area of calculus, specifically integration techniques.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply integration by parts, defining \(u\) and \(dv\) but questions whether their choices are correct. Other participants suggest reconsidering the choice of \(dv\) and clarify what \(v\) should be.

Discussion Status

The discussion is active, with participants providing feedback on the original poster's approach. There is a constructive exchange regarding the correct setup for integration by parts, indicating a productive direction without reaching a consensus on the final method.

Contextual Notes

Participants are navigating the constraints of integration techniques and ensuring the correct interpretation of the integral's components.

duki
Messages
264
Reaction score
0

Homework Statement


Integrate [tex]\int{\frac{lnx}{x^4}dx}[/tex]


Homework Equations



The Attempt at a Solution



I get this:
[tex]u = ln x, du = \frac{1}{x}[/tex]
[tex]dv=x^4, v=\frac{x^5}{5}dx[/tex]
[tex]\frac{(lnx)x^5}{5}-\int{\frac{x^5}{5}*\frac{1}{x}dx} = \frac{(lnx)x^5}{5}-\frac{6x^6}{5}dx}[/tex]


Am I doing this right?
 
Physics news on Phys.org
Your dv should be the integral of 1/x^4, not x^4.
 
Hmm, ok. So what would be v?
 
The integral of x^(-4), which is 1/-3 * x^-3
 
Oooh, ok. Thanks for your help!
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 105 ·
4
Replies
105
Views
11K
Replies
4
Views
3K
Replies
3
Views
2K
  • · Replies 22 ·
Replies
22
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
2
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K