What Is the Integral of e^-(constant)x^2?

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SUMMARY

The integral of e^-(constant)x^2 cannot be expressed in a simple closed form. Instead, it is represented using the error function, commonly denoted as "erf". The discussion emphasizes that for the specific case where the constant equals 1/2, the integral can be evaluated using standard forms related to the error function. This highlights the limitations of elementary functions in expressing certain integrals.

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  • Understanding of integral calculus
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  • Knowledge of Gaussian integrals
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Need the integral of e^-(constant)x^2...don't want to use Gauss integral trick
 
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The indefinite integral cannot be expressed in simple form. Usually it is given in terms of a function called "erf", which is simply a standard form (constant=1/2) integral.
 

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