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Prompt: Write a Python script for mathematical integration and format as LaTeX

Here is the Python implementation using **SciPy** and **SymPy** for numerical and symbolic integration:

```python

import sympy as sp

from scipy import integrate

x = sp.Symbol('x')

f = sp.exp(-x**2)

exact_result = sp.integrate(f, (x, 0, sp.oo))

print(f"Exact Result: {exact_result}")

res, err = integrate.quad(lambda x: sp.exp(-x**2), 0, float('inf'))

print(f"Numerical Result: {res}")

```

Mathematical Formula

The Gaussian integral equation is represented as:

Performance Comparison Matrix

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