# integration of sec x tan x

#### Understand the Problem

The question is asking for the integral of the function sec(x)tan(x), which is a common integral in calculus. It is seeking the antiderivative of this expression.

$\text{sec}(x) + C$

The final answer is $\int ext{sec}(x) ext{tan}(x) , dx = ext{sec}(x) + C$

#### Steps to Solve

1. Recognize the integral of a basic function

The function $ext{sec}(x) ext{tan}(x)$ is a known derivative in calculus. Specifically, it is the derivative of the secant function:

$$\frac{d}{dx}[ ext{sec}(x)] = ext{sec}(x) ext{tan}(x)$$

1. Use the basic integral rule

Since we recognize that $ext{sec}(x) ext{tan}(x)$ is the derivative of $ext{sec}(x)$, the integral of $ext{sec}(x) ext{tan}(x)$ will be the original function $ext{sec}(x)$ plus a constant of integration $C$.

Therefore, the integral of $ext{sec}(x) ext{tan}(x)$ is:

$$\int ext{sec}(x) ext{tan}(x) , dx = ext{sec}(x) + C$$

The final answer is $\int ext{sec}(x) ext{tan}(x) , dx = ext{sec}(x) + C$

Integrating the function $\text{sec}(x)\text{tan}(x)$ gives us the antiderivative $\text{sec}(x)$, which is a common result in calculus.
A common mistake is forgetting to add the constant of integration $C$. Always remember to include it when finding antiderivatives.