Integral for Multiple Natural Logs

In summary, the integral for multiple natural logs is a mathematical expression that represents the area under the curve of a function that contains multiple natural logarithmic terms. It is calculated using integration techniques such as integration by parts, substitution, or partial fractions. Some common examples of functions that contain multiple natural logarithmic terms include ln(x), ln(x^2), ln(x^3), etc. This integral is important in scientific research as it allows for the calculation of areas under curves in functions that contain multiple natural logarithmic terms, with applications in various fields. There are special properties of the integral, such as the logarithmic integration property.
  • #1
Dragon M.
3
0

Homework Statement



I need to find whether or not the Ʃ1/(n(ln n)(ln(ln(n)))) (from 2 to infinity) converges or diverges using the Integral test. I think the best question to ask is where to start with the integral?


Homework Equations



None.


The Attempt at a Solution



I've tried integrating by parts, but I can't find du or v for 1/(lnx)ln(ln(x)). Is there a way to simplify this into a more friendly form?
 
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  • #2
If you let u= ln(ln(x)) then [itex]du= (1/ln(x))(1/x)dx[/itex].
 

1. What is the integral for multiple natural logs?

The integral for multiple natural logs is a mathematical expression that represents the area under the curve of a function that contains multiple natural logarithmic terms.

2. How is the integral for multiple natural logs calculated?

The integral for multiple natural logs is calculated using integration techniques such as integration by parts, substitution, or partial fractions.

3. What are some common examples of functions that contain multiple natural logarithmic terms?

Some common examples of functions that contain multiple natural logarithmic terms include ln(x), ln(x^2), ln(x^3), etc.

4. What is the importance of the integral for multiple natural logs in scientific research?

The integral for multiple natural logs is important in scientific research as it allows for the calculation of areas under curves in functions that contain multiple natural logarithmic terms. This has applications in many fields such as physics, biology, and economics.

5. Are there any special properties of the integral for multiple natural logs?

Yes, there are special properties of the integral for multiple natural logs, such as the logarithmic integration property which states that the integral of ln(x) is xln(x) - x + C.

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