What is the integral of $e^(2x^2)$ ?

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Answer 1 · 2015-08-03T13:04:14

$int e^(2x^2) dx$ cannot be expressed using elementary functions. You need the imaginary error function, erfi(x).

The imaginary error function is $2/sqrtpi int e^(x^2) dx$

$int e^(2x^2) dx$ can be intergrated using substitution $u = sqrt2 x$ so $du = sqrt2 dx$ and we get:

$int e^(2x^2) dx = 1/sqrt2 int e^(u^2) du$

$= 1/sqrt2 sqrtpi/2 "erfi" u +C$

$= sqrt(2pi)/4 "erfi"(sqrt2x) +C$

What is the integral of e^(2x^2)e^(2x^2)?