Integral of $$$\csc^{2}{\left(x \right)}$$$

Find $$$\int \csc^{2}{\left(x \right)}\, dx$$$.

The integral of $$$\csc^{2}{\left(x \right)}$$$ is $$$\int{\csc^{2}{\left(x \right)} d x} = - \cot{\left(x \right)}$$$:

$${\color{red}{\int{\csc^{2}{\left(x \right)} d x}}} = {\color{red}{\left(- \cot{\left(x \right)}\right)}}$$

Therefore,

$$\int{\csc^{2}{\left(x \right)} d x} = - \cot{\left(x \right)}$$

Add the constant of integration:

$$\int{\csc^{2}{\left(x \right)} d x} = - \cot{\left(x \right)}+C$$

Answer: $$$\int{\csc^{2}{\left(x \right)} d x}=- \cot{\left(x \right)}+C$$$