How can I determine if a given integral is solvable?

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Discussion Overview

The discussion revolves around determining the solvability of integrals, exploring methods and tools for evaluating whether a given integral can be solved or expressed in terms of elementary functions. Participants share their experiences and suggest various approaches, including conventional methods and online tools.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests starting with conventional methods such as integration by parts, substitutions, and partial fraction decomposition to assess solvability.
  • Another participant mentions consulting "Gradsteyn & Rythzik" for integrals that are not solvable by conventional methods.
  • There is a mention of the Wolfram Integrator as a quick reference tool for evaluating integrals.
  • One participant expresses skepticism about the Wolfram Integrator's effectiveness, particularly for complex integrals, citing personal experiences where it failed to provide useful results.
  • A participant shares a specific integral related to the Laplace Transform of arctangent and discusses their attempt to find its antiderivative using the theorem of Leibniz & Newton.
  • Another participant confirms success with the same integral when entered correctly into the Wolfram Integrator, indicating that input accuracy may affect results.
  • There is a light-hearted exchange about the potential for miscommunication or errors in using online tools, with a suggestion that the Wolfram team may be introducing their own mathematical conventions.

Areas of Agreement / Disagreement

Participants express differing views on the reliability of the Wolfram Integrator, with some finding it useful while others have had negative experiences. There is no consensus on the best method for determining the solvability of integrals, as various approaches are discussed.

Contextual Notes

Participants note that the effectiveness of methods and tools may depend on the specific integral being evaluated and the accuracy of input provided to computational tools.

bomba923
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Ok...now how do I know if a certain integral is solv/integrat-able or not?
Just by looking at the inside function, how can I tell if the integral can be solved or not??
 
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How about these steps:

1.Try conventional methods:part integration,substitutions,partial fraction decompositions,residues theorem.

2.If it doesn't work,then search for it in "Gradsteyn & Rythzik".

3.If it's not there,the primitive/anitderivative exists,but it's not expressible through elementary functions.

Daniel.
 
Trust me,that one is useless for nasty integrals.I tried it for about 3 times over the last month and it wouldn't give me anything...


Daniel.
 
dextercioby said:
Trust me,that one is useless for nasty integrals.I tried it for about 3 times over the last month and it wouldn't give me anything...


Daniel.
Really? Can you give me an example please.
 
I tried an integral that comes up in the Laplace Transform of arctangent

[tex]\int_{0}^{+\infty} e^{-sx}\arctan x dx[/tex]

Of course,i asked for the antidifferential,i thought i could apply the theorem of Leibniz & Newton myself...

Daniel.
 
dextercioby said:
I tried an integral that comes up in the Laplace Transform of arctangent

[tex]\int_{0}^{+\infty} e^{-sx}\arctan x dx[/tex]

Of course,i asked for the antidifferential,i thought i could apply the theorem of Leibniz & Newton myself...

Daniel.

Works fine for me when I enter:

Code: 
Exp[-s x] ArcTan[x]
 
Thenx,Zurtex,there's no wonder i couldn't do it... :-p I misstyped something...
I like the result,though... :-p

Daniel.
 
dextercioby said:
Thenx,Zurtex,there's no wonder i couldn't do it... :-p I misstyped something...
I like the result,though... :-p

Daniel.
Yeah I can't help thinking Wolfram are trying to introduce their own brand of maths :wink:
 

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