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.
Answer
$\text{sec}(x) + C$
Answer for screen readers
The final answer is $\int ext{sec}(x) ext{tan}(x) , dx = ext{sec}(x) + C$
Steps to Solve
- 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:
$$\frac{d}{dx}[ ext{sec}(x)] = ext{sec}(x) ext{tan}(x)$$
- 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 $\int ext{sec}(x) ext{tan}(x) , dx = ext{sec}(x) + C$
More Information
Integrating the function $\text{sec}(x)\text{tan}(x)$ gives us the antiderivative $\text{sec}(x)$, which is a common result in calculus.
Tips
A common mistake is forgetting to add the constant of integration $C$. Always remember to include it when finding antiderivatives.
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