Anyway, the title of the webpage would be How to Solve the Integral (x+1/x+2)+3.

  • Thread starter mikel542
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    Integration
In summary, the conversation revolves around integration and a specific problem involving an integral sign and various terms. There is some disagreement on how to approach the problem, with one person suggesting to divide one of the terms and another person suggesting to integrate each term separately. The conversation ends with someone possibly giving the solution to the problem.
  • #1
mikel542
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Integration

find


(integral sign)= (x+1/x+2)+3
 
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  • #2
If (x+1/x+2) is one term (not sure you have written it correctly), ((x+1/x+2)^2)/2 +3x

You raise the term to the next power and divide the whole thing by that power.
 
  • #3
strongmotive said:
If (x+1/x+2) is one term (not sure you have written it correctly), ((x+1/x+2)^2)/2 +3x

You raise the term to the next power and divide the whole thing by that power.

Dead wrong. Differentiate that and use the chain rule. It doesn't work. You have to integrate each term separately. Integrate x, 1/x, 2 and 3 and add the results.
 
  • #4
mikel542 said:
Integration

find


(integral sign)= (x+1/x+2)+3

What exactly is the problem? "(integral sign) = <whatever>" makes no sense to me. Is this the problem?
[tex]\int (\frac{x + 1}{x + 3} + 3)dx[/tex]

Or is this it?
[tex]\int (x + 1/x + 2 + 3)dx[/tex]
I suspect that this is not what you meant, although Dick interpreted what you wrote that way.

If the first integral is the one you meant, you'll need to divide (x + 1) by (x + 2), which will give you 1 + (some number)/(x + 2).
 
  • #5
Mark44 said:
What exactly is the problem? "(integral sign) = <whatever>" makes no sense to me. Is this the problem?
[tex]\int (\frac{x + 1}{x + 3} + 3)dx[/tex]

Or is this it?
[tex]\int (x + 1/x + 2 + 3)dx[/tex]
I suspect that this is not what you meant, although Dick interpreted what you wrote that way.

If the first integral is the one you meant, you'll need to divide (x + 1) by (x + 2), which will give you 1 + (some number)/(x + 2).

to thread starter :
if it is the first integral that Mark is referring to, you should most probably get 4x-ln(x+2)
 
  • #6
icystrike said:
to thread starter :
if it is the first integral that Mark is referring to, you should most probably get 4x-ln(x+2)

I'm not sure giving the answer is really the way we give help here, is it?
 

What is an integral?

An integral is a mathematical concept that represents the area under a curve in a graph. It is used to solve problems involving continuous quantities, such as distance, speed, and volume.

How do you solve an integral?

To solve an integral, you need to use a specific method called integration. This involves finding the anti-derivative of the function and then evaluating it at the limits of integration.

What is the function in the integral (x+1/x+2)+3?

The function in this integral is (x+1/x+2)+3. It is a rational function, meaning that it is a ratio of two polynomials, and it includes both a variable (x) and a constant (3).

What is the purpose of the +3 at the end of the integral?

The +3 at the end of the integral is a constant term. It is added to the result of the integration and does not affect the process of solving the integral.

Can this integral be solved using basic rules?

Yes, this integral can be solved using basic integration rules, such as the power rule, product rule, and chain rule. It can also be solved using techniques such as substitution, integration by parts, and partial fractions.

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