Integral of erf(x)

Here I talked about special functions, and at the end of the post I said I would explain how to integrate these special functions. So here I am, showing you how to integrate the error function erf(x). If you gave it a try, let me know in the comments if you used this approach!

The only technique that is going to work is integration by parts. We know that erf(x) is equal to the integral of e^(-x^2), so the derivative of erf(x) is e^(-x^2).

We can solve this integral using u-substitution.

Overall:

And that’s it!

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