Can anyone solve this complicated integral with limited conditions?

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In summary, the conversation is about the struggle to find a method or approach to break down a complex integral with limits and parameters. The person has tried various methods, including breaking it down to real and imaginary parts, but has not been successful. Mathematica also indicates that the integral does not converge.
  • #1
rman144
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I've looked everywhere for a method or approach to break down this integral, but so far, nothing. If anyone has any ideas or answers, I would be incredibly thankful:


∫ {[ln(v)]^(s-1) - [ln(v)]^(-s)}/(v-1) dv, with limits from v=1 to v=e, and 0<Re(s)<1

I've tried breaking it down to the real and imaginary parts, but even then I was back to the problem of trying to integrate with cos(u)+isin(u) issues.
 
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  • #2
[tex]\int_1^e \frac{(\ln v)^{s - 1} - (\ln v)^{-s}}{v - 1} \,dv

According to Mathematica, the integral doesn't converge. It doesn't seem to be able to find an indefinite integral either.
 

1. What is an integral with complications?

An integral with complications is a type of mathematical integral that is more complex than a basic integral. It may involve multiple variables, non-standard functions, or other complications that make it difficult to solve using traditional methods.

2. How is an integral with complications different from a regular integral?

An integral with complications is different from a regular integral in that it requires a more advanced approach to solve. A regular integral can be solved using basic integration techniques, such as substitution or integration by parts, but a complicated integral may require more specialized methods.

3. What are some common types of complications in integrals?

Some common types of complications in integrals include multiple variables, improper integrals, trigonometric functions, logarithmic functions, and infinite limits of integration.

4. How do you solve an integral with complications?

Solving an integral with complications involves using advanced integration techniques, such as partial fractions, trigonometric substitutions, or integration by parts. It may also require the use of specialized software or numerical methods to approximate the solution.

5. Why are integrals with complications important in science?

Integrals with complications are important in science because they allow us to model and understand complex systems and phenomena. These integrals often arise in physics, engineering, and other scientific fields when trying to solve real-world problems and make predictions. They are also important in developing new mathematical techniques and advancing our understanding of mathematics itself.

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