Integral of e to the power of x^-2

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SUMMARY

The integral of e to the power of x^-2, evaluated from 0 to x/√2, does not have a solution in terms of elementary functions. This fact is well-documented in calculus literature. However, this integral is frequently utilized in statistics and can be approximated using the Gaussian function or the error function (erf). For further details, refer to the error function documentation.

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Tom.M
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Hi
can anyone help me with this integral ?

the integral of e to the power of x^-2, and this integral from 0 to x/√2

thanks
 
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There is no answer in terms of elementary functions. This is a fact in probably every calculus book. However, the integral is used commonly in statistics, and so it can be evaluated using a Gaussian or the erf (error) function:

http://en.wikipedia.org/wiki/Error_function
 

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