Integralen av $$$\csc^{2}{\left(x \right)}$$$

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

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

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

Alltså,

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

Lägg till integrationskonstanten:

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

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