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:

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

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