Sympy计算复杂定积分超时咨询：是否无闭式解？

我尝试用Sympy计算一个定积分，代码如下：

import sympy as sp
import math

eps, psi = sp.symbols("eps psi", positive=True)
y = 1 / (math.sqrt(8)*math.pi**2)*sp.integrate(1/sp.sqrt(eps - psi) * d2crho_dpsi2, (psi, 0, eps))

其中d2crho_dpsi2是预计算的关于psi的复杂表达式，具体形式如下：

(110826921669719*(-110826921669719*psi**2/(500000000000000*(1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)**2*(-74440218185373*psi/500000000000000 - LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000))**2) - 20*psi/((1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)**3*(-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)))*(-110826921669719*psi**3*log(1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)/(25000000000000*(-74440218185373*psi/500000000000000 - LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000))**3) + 74440218185373*psi**2/(2500000000000*(1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)*(-74440218185373*psi/500000000000000 - LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000))**2) + 134335984549343*psi/(200000000000*(1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)**2*(-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)))/(500000000000000000*(-110826921669719*psi**2*log(1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)/(5000000000000000*(-74440218185373*psi/500000000000000 - LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000))**2) + psi/((1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)*(-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)))**2) + (65999841839257*psi**3/(100000000000000*(1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)**2*(-74440218185373*psi/500000000000000 - LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000))**3) + 886615373357751*psi**2/(100000000000000*(1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)**3*(-74440218185373*psi/500000000000000 - LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000))**2) + 600*psi/((1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)**4*(-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)))/(-74440218185373*psi**2*log(1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)/(50000000000000*(-74440218185373*psi/500000000000000 - LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000))**2) + 134335984549343*psi/(2000000000000*(1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)*(-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000))))/(-74440218185373*psi**2*log(1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)/(50000000000000*(-74440218185373*psi/500000000000000 - LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000))**2) + 134335984549343*psi/(2000000000000*(1 + (-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)/psi)*(-psi - 134335984549343*LambertW(-74440218185373*psi*exp(-74440218185373*psi/500000000000000)/500000000000000)/20000000000000)))

运行代码长达一小时仍未得到结果，请问是被积函数过于复杂导致sympy无法计算，还是该积分不存在闭式解？

内容的提问来源于stack exchange，提问作者ellipse314