I am trying to show that $erf(\sqrt x)=1/\sqrt\pi$ (integral from $t$ to $0$) of $e^{-t}/\sqrt t dt$
I have used the definition of $erf(x) = 2/\sqrt\pi$ (integral from $t$ to $0$) $e^{-t^2} dt$ and used a $u$-substitution and get the answer that I'm looking for in terms of $u$ (which in my substitution is $=x^2$). Is this right? Is it ok that my answer is not converted back to $x$. I'm not really experienced with the error function and am not sure if I'm missing something...