Integral of e^(2x) - Step-by-Step Solution | ML for Beginners

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Answer:

Step-by-Step Solution

Step 1

Use substitution: let u = 2x, then du = 2dx, so dx = du/2

Step 2

Factor out the constant

Step 3

Integrate e^u

Step 4

Substitute back u = 2x

🤖 Machine Learning Application

Exponential functions are fundamental to machine learning! e^(2x) appears in softmax activation functions, exponential learning rate schedules, and the mathematical foundation of neural network backpropagation. The integral is used in deriving probability distributions like the exponential and Laplace distributions.

Frequently Asked Questions

What is the integral of e^(2x)?

The integral of e^(2x) is \frac{1}{2}e^{2x} + C, where C is the constant of integration.

How do you solve this integral?

Follow the step-by-step solution above, which uses u-substitution.

Where is this used in machine learning?

Exponential functions are fundamental to machine learning! e^(2x) appears in softmax activation functions, exponential learning rate schedules, and the mathematical foundation of neural network backpropagation. The integral is used in deriving probability distributions like the exponential and Laplace distributions.