# calculus and analysis – Extracting integral from MeijerG

MMA can find the identity of the following integral
$$int_0^infty textrm{e}^{-(x/t)^2-t}textrm{d}t text{for x>0} tag{1}$$
with a Meijer G function
$$frac{1}{sqrt{pi}}G_{0,,3}^{3,,0} left( {begin{array}{*{20}c} {} \ {0,frac{1}{2},1} \ end{array};left| {;frac{{x^{,2} }}{4}} right.} right) tag{2}$$

``````FullSimplify(Integrate(Exp(-(x/t)^2 - t), {t, 0, ∞}), x > 0)
``````

output:

``````MeijerG({{}, {}}, {{0, 1/2, 1}, {}}, x^2/4)/Sqrt(π)
``````

How can be done the opposite way, i.e. I know eq.(2) but want to get eq.(1)?

MMA 12.1