# What is the antiderivative of cos x?

#### Understand the Problem

The question is asking for the antiderivative, or indefinite integral, of the function cos(x). The antiderivative will give us a function whose derivative is cos(x).

The antiderivative of $cos(x)$ is $sin(x) + C$.

The antiderivative of $cos(x)$ is $sin(x) + C$.

#### Steps to Solve

1. Identify the function to integrate

We need to find the antiderivative of $cos(x)$. This means we are looking for a function $F(x)$ such that $F'(x) = cos(x)$.

1. Recall the antiderivative of cosine

The antiderivative of $cos(x)$ is a known result. We use the fact that:

$$\int cos(x) , dx = sin(x) + C$$

where $C$ is the constant of integration.

1. Write down the final result

Now we can formally state the result of our integration:

$$F(x) = sin(x) + C$$

This tells us that the indefinite integral of $cos(x)$ is $sin(x)$ plus a constant.

The antiderivative of $cos(x)$ is $sin(x) + C$.

The constant $C$ represents an arbitrary constant that arises from indefinite integrals, indicating that there are infinitely many functions with the same derivative.
• A common mistake is forgetting to include the constant of integration, $C$. Always remember to add it when calculating indefinite integrals.