How to Calculate Antiderivatives: A Step-by-Step Guide

Learning how to calculate an antiderivative is a foundational skill in calculus. Essentially, you are reversing the process of differentiation to find the original function. If you are given a derivative, finding the antiderivative gives you the indefinite integral.

Step 1: Identify the Integration Rule

To find an antiderivative, you first need to recognize the form of your function. The most common rule is the Power Rule. For any term x^n (where n is not -1), you add 1 to the exponent and divide by the new exponent.

Step 2: Integrate Term by Term

If your expression has multiple terms separated by addition or subtraction, you can calculate the antiderivative of each term individually. For example, to integrate 3x^2 + 2x, you apply the Power Rule to 3x^2 and 2x separately.

Step 3: Always Add the Constant of Integration

Because the derivative of any constant number (like 5, 10, or -3) is zero, we must acknowledge that infinitely many functions could share the same derivative. Always append "+ C" to your final answer to represent this constant of integration.

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