# What is the antiderivative of cos?

#### Understand the Problem

The question is asking for the antiderivative of the cosine function, which is a fundamental concept in calculus. To solve this, we will identify the function whose derivative is cosine.

#### Answer

$$\int \cos(x) \, dx = \sin(x) + C$$
##### Answer for screen readers

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

#### Steps to Solve

1. Identify the Function

We need to find a function, $F(x)$, such that its derivative equals $\cos(x)$. This leads us to set up the equation:

$$F'(x) = \cos(x)$$

1. Recall the Antiderivative of Cosine

From differentiation rules, we know that the derivative of $\sin(x)$ is $\cos(x)$. Therefore, we conclude that the antiderivative of $\cos(x)$ is:

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

where $C$ is the constant of integration.

1. Conclude with the Result

Thus, we express the complete solution for the antiderivative:

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

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

#### More Information

The function $\sin(x)$ is integral to many areas in mathematics and physics. The constant $C$ represents an infinite number of functions that differ by a constant, all having the same derivative.

#### Tips

• Forgetting to include the constant of integration $C$ when determining the antiderivative.
• Confusing $\sin(x)$ with $\cos(x)$ in terms of their derivatives.
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