Integral of $$$\sec{\left(\theta \right)}$$$ with respect to $$$x$$$

Find $$$\int \sec{\left(\theta \right)}\, dx$$$.

Apply the constant rule $$$\int c\, dx = c x$$$ with $$$c=\sec{\left(\theta \right)}$$$:

$${\color{red}{\int{\sec{\left(\theta \right)} d x}}} = {\color{red}{x \sec{\left(\theta \right)}}}$$

Therefore,

$$\int{\sec{\left(\theta \right)} d x} = x \sec{\left(\theta \right)}$$

Add the constant of integration:

$$\int{\sec{\left(\theta \right)} d x} = x \sec{\left(\theta \right)}+C$$

$$$\int \sec{\left(\theta \right)}\, dx = x \sec{\left(\theta \right)} + C$$$A