Integrating (ln x)^2/e^5t in Variation of Parameters Problem

  • Context: Undergrad 
  • Thread starter Thread starter eagleswings
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the integration of the expression (ln x)^2/e^(5t) in the context of a variation of parameters problem. Participants explore the integration techniques applicable to this expression, including the potential use of integration by parts.

Discussion Character

  • Technical explanation, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant questions whether (ln x)(ln x) can be simplified to ln(x^2) or another form, expressing uncertainty about the integration process.
  • Another participant clarifies the expression, questioning if it is e^(5t) or e^(5x), suggesting that the latter may not have a closed form solution, while the former could be more manageable.
  • A participant confirms that the expression is indeed e^(5x) and expresses intent to use the previous suggestions for integration.
  • One participant provides a link to an integral calculator, noting that the resulting integral is complex and not easily readable.
  • A later reply expresses difficulty in understanding the output from the integral calculator, indicating unfamiliarity with some of the symbols used.

Areas of Agreement / Disagreement

Participants generally agree on the complexity of the integral and the challenges involved in integrating the expression, but there is no consensus on the best approach or the nature of the solution.

Contextual Notes

There are unresolved questions regarding the simplification of ln(x)^2 and the specific integration techniques applicable to the expression, as well as the potential for closed form solutions depending on the variable used in the exponent.

eagleswings
Messages
15
Reaction score
1
i have to integrate (ln x)(ln x)/ e^5t [in a variation of parameters problem] and have looked everywhere to see if Ln x multiplied by itself can be shortened to something like ln x^2 or some other reasonable thing but can't find such a rule anywhere. do i have to do this the long way with integration by parts? not even sure what to do with three things in integration by parts.
 
Physics news on Phys.org
Is it e^5t or e^5x?. If it's the latter I don't believe there's a closed form solution, but if it's the former, then it's more doable.

Let u = lnx, du= dx/x, dv=lnxdx, v = xlnx - x (Verify this by IBP). Then all the integrals are doable.

And yes, there are no identities to simplify ln(x)^2.
 
yes actually it is e^5x. all the t's that go into the integral have to change to x. but perhaps i can start with what you gave me - thanks!
 
man, i can'te even read that one. it's got symbols i haven't seen used, maybe they are just variables, but unusual ones. maybe i learn that next year! sigh.
 

Similar threads

  • · Replies 16 ·
Replies
16
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 8 ·
Replies
8
Views
4K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K