Integral of $$$\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}}$$$

Find $$$\int \frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}}\, dx$$$.

Simplify the integrand:

$${\color{red}{\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x}}} = {\color{red}{\int{1 d x}}}$$

Apply the constant rule $$$\int c\, dx = c x$$$ with $$$c=1$$$:

$${\color{red}{\int{1 d x}}} = {\color{red}{x}}$$

Therefore,

$$\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x} = x$$

Add the constant of integration:

$$\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x} = x+C$$

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