Integral of e^(x²) - Step-by-Step Solution | ML for Beginners

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Step-by-Step Solution

Step 1

This integral has no elementary closed form

Step 2

Can be expressed using the error function

Step 3

For definite integrals over all reals

🤖 Machine Learning Application

The Gaussian function e^(-x²) is the foundation of normal distributions, crucial to ML. Used in Gaussian processes, kernel methods, and probability theory underlying many ML algorithms.

Frequently Asked Questions

What is the integral of e^(x²)?

The integral of e^(x²) is \text{No elementary form (error function)}, where C is the constant of integration.

How do you solve this integral?

Follow the step-by-step solution above, which uses standard integration techniques.

Where is this used in machine learning?

The Gaussian function e^(-x²) is the foundation of normal distributions, crucial to ML. Used in Gaussian processes, kernel methods, and probability theory underlying many ML algorithms.