# Evaluate the integral. {eq}\int \frac{\sec \theta}{\sec \theta - \cos \theta} \, \mathrm{d} \theta {/eq}

## Question:

Evaluate the integral.

{eq}\int \frac{\sec \theta}{\sec \theta - \cos \theta} \, \mathrm{d} \theta {/eq}

## Indefinite Integral in Calculus:

The process of finding a function when it's derivetive is given is called anti-differentiation or integration. The symbol {eq}\int {/eq} represents integration, and {eq}dx {/eq} is a differential of the variable {eq}x {/eq} , which is a very small width of {eq}x {/eq}.

To solve this problem, we'll use apply trig-ratio {eq}\displaystyle \sec\theta= \frac{1}{ \cos \theta} {/eq}and apply trig-substitution {eq}1 - \cos^2 \theta=\sin^2 \theta {/eq}

## Answer and Explanation: 1

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We are given:

{eq}\displaystyle \int \dfrac{\sec \theta}{\sec \theta - \cos \theta} \, \mathrm{d} \theta {/eq}

Apply trig-ratio {eq}\displaystyle...

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