ulln.py

from sympy import *
init_printing(use_unicode=False, wrap_line=False, no_global=True)

x = Symbol('x', positive=True)
xmax = Symbol('xmax', positive=True)
sigma = Symbol('sigma', positive=True)
mu = Symbol('mu')

lx = log(x)-log(xmax-x)

pdf = exp(-0.5 * ((lx - mu)/sigma)**2) / (sqrt(2*pi) * sigma)
E = integrate(pdf*x,(x,0,xmax))


#----------------------

from sympy import *
init_printing(use_unicode=False, wrap_line=False, no_global=True)

lx = Symbol('lx')
xmax = Symbol('xmax', positive=True)
sigma = Symbol('sigma', positive=True)
mu = Symbol('mu')

x = xmax*exp(lx)/(exp(lx)+1)

pdf = exp(-0.5 * ((lx - mu)/sigma)**2) / (sqrt(2*pi) * sigma)
E = integrate(pdf*x,(lx,-oo,oo))