Integrating x/(x+2): Tips and Tricks for Solving This Tricky Integral

In summary, integration involves finding the area under a curve by using mathematical techniques to manipulate an equation into a form that can be easily integrated. The specific equation for the integration of (x/(x+2)) is ∫ (x/(x+2)) dx, and the process for solving it may involve substitution, integration by parts, or partial fractions. Integration has various real-life applications, such as calculating distance and volume, and is used in fields such as physics, engineering, and economics. The integration of (x/(x+2)) may differ from other integration problems in terms of the techniques and limits of integration used.
  • #1
pinky86
4
0
[SOLVED] Integration of (x/(x+2))

I've tried integrating x/(x+2). but seem to be going round in circles. I've tried integrating by parts and it didn't work. i was wondering does anyone know what way to do this.
 
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  • #2
Are you trying to differentiate it or integrate it?
 
  • #3
integrating. sorry
 
  • #4
How about a substitution?
 
Last edited:
  • #5
nope didn't try that. thank you!
 
  • #6
pinky86 said:
nope didn't try that. thank you!
No problem, let me know when you get your answer :smile:
 

FAQ: Integrating x/(x+2): Tips and Tricks for Solving This Tricky Integral

What is the formula for integrating (x/(x+2))?

The formula for integrating (x/(x+2)) is ∫ (x/(x+2)) dx = ln|x+2| + C.

How do you solve the indefinite integral of (x/(x+2))?

To solve the indefinite integral of (x/(x+2)), you can use the substitution method. Let u = x+2, then du = dx and the integral becomes ∫ (x/(x+2)) dx = ∫ (1/u) du = ln|u| + C = ln|x+2| + C.

Can you use the power rule to integrate (x/(x+2))?

No, the power rule cannot be used to integrate (x/(x+2)) because the function is not in the form of x^n.

What is the domain and range of the integrated function of (x/(x+2))?

The domain of ln|x+2| is all real numbers except x = -2, and the range is all real numbers.

Is there any other method to integrate (x/(x+2)) besides substitution?

Yes, you can also use partial fractions to integrate (x/(x+2)). First, write the function as (x+2)/(x+2)^2 = 1/(x+2) and then use the partial fraction decomposition to solve the integral. This method can sometimes be easier and faster than substitution.

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