• Support PF! Buy your school textbooks, materials and every day products Here!

Integral - Algebraic Manipulation?

  • Thread starter Prologue
  • Start date
  • #1
185
1

Homework Statement



[tex]\int \frac{x}{x+d}dx[/tex]

The Attempt at a Solution



I tried parts and that turned out horribly so I fired up maple. First move it makes is 'Rewrite Rule'. I've never heard of a rewrite rule but I supposed it could be some algebraic massaging. I ended up looking at it this way:

[tex]\frac{x}{x+d} = 1-1+\frac{x}{x+d} = \frac{x+d}{x+d}-\frac{x+d}{x+d}+\frac{x}{x+d} = \frac{x+d}{x+d}+\frac{x-d-x}{x+d} = 1-\frac{d}{x+d}[/tex]

Which then is easily integrable. My question is, is there a snappier way to think of this/do it?
 

Answers and Replies

  • #2
Defennder
Homework Helper
2,591
5
Just divide x by x+d and you'll get the term on the rightmost of your equalities.
 
  • #3
185
1
As in polynomial long division?

edit: Or is there some way that is easy to see what will happen? Basically it isn't straight up intuitive for me to realize that x/x+d is 1-d/x+d, I'm trying to find a quick method to deal with it.
 
Last edited:
  • #4
1,752
1
[tex]\int\frac{x+d-d}{x+d}dx[/tex]

Break it and integrate.
 
  • #5
185
1
That's much shorter than what I did, thanks.
 

Related Threads for: Integral - Algebraic Manipulation?

  • Last Post
Replies
1
Views
1K
Replies
5
Views
4K
Replies
1
Views
2K
Replies
4
Views
956
  • Last Post
Replies
4
Views
1K
Replies
4
Views
989
  • Last Post
Replies
4
Views
2K
Replies
4
Views
871
Top