Integration by Parts: Solving 1/(u²(a+bu)²) with Substitution

Click For Summary

Homework Help Overview

The problem involves integrating the expression 1/(u²(a+bu)²), where a and b are constants and u is the variable. The discussion centers around the appropriate techniques for integration, particularly focusing on integration by parts and substitution methods.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the potential use of integration by parts and substitution, with some confusion regarding the terminology used. There is mention of partial fraction decomposition as an alternative approach to simplify the integration process.

Discussion Status

The discussion is ongoing, with participants exploring different methods for solving the integral. Some guidance has been offered regarding the use of partial fractions, but there is no consensus on the best approach yet.

Contextual Notes

There is some confusion regarding the terminology, specifically the mention of "substitution by parts," which has led to questions about the correct techniques to apply. Participants are considering various methods without a clear resolution at this stage.

nonechelon
Messages
4
Reaction score
0

Homework Statement



1/(u²(a+bu)²) a and b are constants u is the variable


Homework Equations





The Attempt at a Solution


i know I am suppose to use substition by parts but i don't know what to use.
thanks for help in advance
 
Physics news on Phys.org
nonechelon said:

Homework Statement



1/(u²(a+bu)²) a and b are constants u is the variable


Homework Equations





The Attempt at a Solution


i know I am suppose to use substition by parts but i don't know what to use.
thanks for help in advance

I'm confused. The title says "Integration by parts". Later on, you said you supposed to use "substitution by parts" which is not a technique I've ever heard of. There's a technique called "substitution".

There's also a technique called "partial fractions" or "partial fraction decomposition" in which you can decompose a complicated rational expression into a sum of simpler rational expressions.

So how are you supposed to do this problem?
 
oops i mean integration by parts i don't know why i said substitution.sorry
 
The best approach would be to decompose the fraction first into it's partial fractions as suggested by Mark44. Then integrate the partial fractions separately.
 

Similar threads

Integral using substitution x = -u
  • · Replies 12 ·
Replies
12
Views
2K
Solving this definite integral using integration by parts
  • · Replies 3 ·
Replies
3
Views
2K
Evaluate the definite integral in the given problem
  • · Replies 1 ·
Replies
1
Views
2K
Using hyperbolic substitution to solve an integral
  • · Replies 18 ·
Replies
18
Views
4K
Energy-momentum tensor perfect fluid raise index
  • · Replies 3 ·
Replies
3
Views
2K
Integrals that keep me up at night
  • · Replies 22 ·
Replies
22
Views
3K
Finding the Fourier cosine series for ##f(x)=x^2##
  • · Replies 4 ·
Replies
4
Views
3K
Substitution and Integration by Parts
  • · Replies 3 ·
Replies
3
Views
2K
An Integral simplification I don't understand
  • · Replies 28 ·
Replies
28
Views
3K
Integration question involving square root
  • · Replies 4 ·
Replies
4
Views
2K