Integral of tan(x) - Step-by-Step Solution | ML for Beginners

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Step-by-Step Solution

Step 1

Rewrite tan(x) as sin(x)/cos(x)

Step 2

Use substitution: let u = cos(x), then du = -sin(x)dx

Step 3

Integrate 1/u

Step 4

Substitute back u = cos(x)

🤖 Machine Learning Application

The tangent function and its integral appear in neural network activation functions and gradient calculations. In machine learning optimization, understanding trigonometric integrals helps in analyzing periodic loss landscapes.

Frequently Asked Questions

What is the integral of tan(x)?

The integral of tan(x) is -\ln|\cos(x)| + C, 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 tangent function and its integral appear in neural network activation functions and gradient calculations. In machine learning optimization, understanding trigonometric integrals helps in analyzing periodic loss landscapes.