- #1

- 128

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For example, how would I know that the integral:

[tex]

\int e^{-x^2} dx

[/tex]

is not solvable?

Thanks in advance

- Thread starter Repetit
- Start date

- #1

- 128

- 1

For example, how would I know that the integral:

[tex]

\int e^{-x^2} dx

[/tex]

is not solvable?

Thanks in advance

- #2

- 1,425

- 1

- #3

morphism

Science Advisor

Homework Helper

- 2,015

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It's usually very difficult. You know how Galois theory helps us determine the solvability of polynomial equations? Well, there is a field of math known as differential Galois theory that can be used to prove that the integral you quoted (for instance) is not solvable, in the sense that it cannot be expressed in terms of elementary functions. Although personally I'm ignorant of its ways!

You can also read the following pdf (which AFAIK was posted on these forums):

http://www.claymath.org/programs/outreach/academy/LectureNotes05/Conrad.pdf [Broken]

You can also read the following pdf (which AFAIK was posted on these forums):

http://www.claymath.org/programs/outreach/academy/LectureNotes05/Conrad.pdf [Broken]

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