Integral of x^2/(x+2) Solution | Evaluate the Integral

  • Thread starter professordad
  • Start date
  • Tags
    Integral
In summary, the conversation discusses how to evaluate the integral of x^2/(x+2) and suggests using polynomial division to simplify the problem. One person suggests setting u = x^2 and another suggests u = x+2, but there is a mistake in the second substitution. The correct solution is given at the end, which is \frac{x^2}{2} - 2x + 4\ln{|x+2|} + C.
  • #1
professordad
18
0

Homework Statement



Evaluate the integral:
[itex]\int \frac{x^2}{x + 2} dx[/itex]

Homework Equations



There aren't any relevant equations...

The Attempt at a Solution



In these type of problems you have to set [itex]u = \text{something}[/itex] so I tried setting [itex]u = x^2[/itex], but then [itex]\text{du} = 2x\text{dx}[/itex] and you can't substitute anything. And if [itex]u = x + 2[/itex] then [itex]\text{du} = 1[/itex] and that's useless.

Also, this problem is from the Swokowski calculus textbook (school starts in two days for me so I'm doing self study :smile: )
 
Last edited:
Physics news on Phys.org
  • #2
Before you do anything, do polynomial division (degree of top >= degree of bottom). Once this is done, it should be trivial to take the integral.
 
  • #3
Try doing some algebra first. You can rewrite that. Polynomial long division.
 
  • #4
In you second substitution, where u = x+2, du = dx not du = 1

If you carry thru with this substitution properly, you can find the desired integral.
 
  • #5
Wow, I can't believe I missed that. Here's what I have from there:

Clearly [itex]\frac{x^2}{x + 2} = x - 2 + \frac{4}{x + 2}[/itex]. So integrating that we have [itex]\frac{x^2}{2} - 2x + 4\ln{|x+2|} + C[/itex] where C is a constant.

Thanks for your help guys! I appreciated it :smile:

Also, to SteamKing, yes, I made a mistake while typing it up.
 
Last edited:

1. What is the formula for finding the integral of x^2/(x+2)?

The formula for finding the integral of x^2/(x+2) is ∫(x^2/(x+2)) dx = x^2ln|x+2| - 2x + C.

2. How do you solve for the constant C in the integral of x^2/(x+2)?

To solve for the constant C, you can use the initial conditions of the problem or evaluate the integral at a specific point.

3. Can the integral of x^2/(x+2) be simplified further?

Yes, the integral can be simplified further by using integration by parts or partial fraction decomposition.

4. What is the domain and range of the integral of x^2/(x+2)?

The domain of the integral of x^2/(x+2) is all real numbers except for x = -2, and the range is all real numbers.

5. How can the integral of x^2/(x+2) be applied in real life?

The integral of x^2/(x+2) can be applied in various fields such as engineering, physics, and economics to solve problems involving rates of change, optimization, and area/volume calculations.

Similar threads

  • Calculus and Beyond Homework Help
Replies
15
Views
735
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
12
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
723
  • Calculus and Beyond Homework Help
Replies
22
Views
1K
  • Calculus and Beyond Homework Help
Replies
8
Views
705
  • Calculus and Beyond Homework Help
Replies
7
Views
606
  • Calculus and Beyond Homework Help
Replies
10
Views
1K
  • Calculus and Beyond Homework Help
Replies
27
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
Back
Top