Integral of $\cot{\left(x \right)} \csc{\left(x \right)}$

Find $\int \cot{\left(x \right)} \csc{\left(x \right)}\, dx$.

The integral of $\cot{\left(x \right)} \csc{\left(x \right)}$ is $\int{\cot{\left(x \right)} \csc{\left(x \right)} d x} = - \csc{\left(x \right)}$:

$${\color{red}{\int{\cot{\left(x \right)} \csc{\left(x \right)} d x}}} = {\color{red}{\left(- \csc{\left(x \right)}\right)}}$$

Therefore,

$$\int{\cot{\left(x \right)} \csc{\left(x \right)} d x} = - \csc{\left(x \right)}$$

Add the constant of integration:

$$\int{\cot{\left(x \right)} \csc{\left(x \right)} d x} = - \csc{\left(x \right)}+C$$

$\int \cot{\left(x \right)} \csc{\left(x \right)}\, dx = - \csc{\left(x \right)} + C$A