Definite integrals of the type gaussian distribution times sqare root of x from 0 to inf give imaginary results whereas the functions are real valued in this interval.
int [sqrt(x)*exp(-(x-1)**2),x,0,inf] ? -0.07..i
int [x**(-1/2)*exp(-(x-1)**2),x,0,inf] ? 0.4..i
By the way I would love to know the correct symbolic integral but not only does wolfram alpha struggle but maxima and me as well.
Edit: I was not specific in that I would like to know the symbolic integral.