How to calculate numerically 10 integrals in Python

I need to calculate deterministically the following sum in python using numeric methods.

I have the following function:

Is there any analogue of scipy.integrate.tplquad that can calculate so many integrals?

Solution

Using sympy

import sympy as sym

x = sym.symbols('x1:11')
expr = sym.prod(x) * sym.exp(-sum(x))
integral = sym.integrate(expr, *((xi, 0, 1) for xi in x))

print(integral) will show you the explicit expression, though integral.factor() will show you a neater form.

(-2 + E)**10*exp(-10)    # E is the mathematical constant

You can also evaluate that whatever precision you want.

>>> integral.evalf()  # this can take an argument `n` for precision digits
1.65960210179703e-6