Expotanial integration exp(ax^n+bx) ?

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Discussion Overview

The discussion centers around the integration of the expression exp(ax^n + bx), exploring various methods and the challenges associated with finding an anti-derivative. The scope includes theoretical considerations and practical integration techniques.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant inquires about methods to integrate exp(ax^n + bx).
  • Another participant asks which methods have already been attempted.
  • A different participant notes that even the simpler case of e^{x^2} does not have an elementary anti-derivative, suggesting that the problem may be complex.
  • The original poster lists several methods they have tried, including integration by parts, substitution, and partial fractions.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the integration methods, and multiple competing views regarding the feasibility of finding an elementary anti-derivative remain unresolved.

Contextual Notes

Limitations include the lack of clarity on specific values for a, b, and n, as well as the potential dependence on the definitions of integration methods used.

s210995
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Hi All

How to integrate this?

exp(ax^n+bx)

Thanks in advance
 
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Which methods have you already tried?

Torquil
 
Even something as simple as [itex]e^{x^2}[/itex] with a= 1, b= 0, n= 2, does not have an elementary anti-derivative.
 
Last edited by a moderator:
I tried the following methods:
by part
by substitution
by partial fraction

thanks
 

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