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

This problem is FRUSTRATING me SO Much!

  • Thread starter BuBbLeS01
  • Start date
602
0
1. Homework Statement
Find the indefinite integral...
X^2/ X-1

In my book they set it up as 2 separate integrals...
X+1 + 1/X-1

I figured they got that from long division but I am not getting that answer. So can someone please tell me how they got those 2 separate integrals
 

Answers and Replies

1,750
1
[tex]\int\frac{x^2}{x-1}dx[/tex]

[tex]\int\frac{x^2-1+1}{x-1}dx[/tex]

[tex]\int\left[\frac{(x+1)(x-1)}{x-1}+\frac{1}{x-1}\right]dx[/tex]

[tex]\int\left(x+1+\frac{1}{x-1}\right)dx[/tex]

Does this make a little more sense?
 
Last edited:
602
0
Yes it makes more sense but I just want to make sure I understand what you did..

In part B you completed the square...(But I thought it would be (X^2 + 1) - 1)
 
1,750
1
I did not complete the square, and plus, you do not have a linear factor - so you shouldn't even consider it.

[tex]x^2-1=(x+1)(x-1)=\mbox{Difference of Squares}[/tex]
 
Last edited:
602
0
Oh....I don't think we've used that before...I will have to look it up...thank you!
 
1,750
1
Oh....I don't think we've used that before...I will have to look it up...thank you!
BuBbLeS, you have used it plenty of times (you learn it in junior high or HS). You just forgot! No worries, go look it up and you'll be like oh yeah ... I remember that :p
 
602
0
I hope so lol!

I have another question on another problem...
I am trying to complete the square...

I have 6x - x^2
Then I did (6/2)^2 = 9
So I end up with (-x^2 + 6x + 9) - 9
I need to end up with 9 - (x - 3)^2
Can I make (-x^2 + 6x + 9) to (x^2 + 6x + 9) because the x is squared so it will be positive or is that negative mean like -(x^2)??
And (x - 3)^2 gets me x^2 - 6x + 9 so I am a little confused...
 
1,750
1
Before you complete the square, make sure that the coefficient of your leading term is a positive one.

[tex]6x-x^2[/tex]

[tex]-(x^2-6x+9-9)[/tex]

[tex]-(x^2-6x+9)+9[/tex]

[tex]9-(x-3)^2[/tex]
 
602
0
Ohhhh....thank you so much!!!
 
1,750
1
So you solved it, yes?
 

Related Threads for: This problem is FRUSTRATING me SO Much!

Replies
2
Views
2K
Replies
10
Views
2K
  • Last Post
Replies
2
Views
952
  • Last Post
Replies
3
Views
1K
Replies
37
Views
4K
  • Last Post
Replies
3
Views
854
  • Last Post
Replies
3
Views
804
  • Last Post
Replies
7
Views
1K
Top