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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

# Symbolic Integration with SymPy
x = sp.Symbol('x')
f = sp.exp(-x**2)
exact_result = sp.integrate(f, (x, 0, sp.oo))
print(f"Exact Result: {exact_result}")

# Numerical Integration with SciPy
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:

$$ \int_{0}^{\infty} e^{-x^2} dx = \frac{\sqrt{\pi}}{2} $$

### Performance Comparison Matrix

> **Pro Tip:** When generating publication-ready documents, preserve code blocks and LaTeX math formatting using Chat2Doc exporter!

Auto preserves code blocks & tablesClient-Side Rendered

Formatted Document Preview:Ready to Export

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

Symbolic Integration with SymPy

x = sp.Symbol('x')

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

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

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

Numerical Integration with SciPy

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:

LaTeX Formula Preserved\int_{0}^{\infty} e^{-x^2} dx = \frac{\sqrt{\pi}}{2}

Performance Comparison Matrix

| :--- | :--- | :--- | :--- |

**Pro Tip:** When generating publication-ready documents, preserve code blocks and LaTeX math formatting using Chat2Doc exporter!

Why Export ChatGPT Conversations to Markdown?

ChatGPT is an incredible assistant for brainstorming, coding, and writing research notes. Exporting to standard Markdown (.md) provides:

Obsidian & Notion Compatibility: Import directly into your second-brain knowledge base.
Preserved Code Blocks: Keep Python, JavaScript, and SQL syntax highlighting ready for IDE paste.
LaTeX Math Support: Academic equations render seamlessly without formatting loss.

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