Integraal van $$$6 \cot{\left(x \right)} \csc{\left(x \right)}$$$
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Uw invoer
Bepaal $$$\int 6 \cot{\left(x \right)} \csc{\left(x \right)}\, dx$$$.
Oplossing
Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=6$$$ en $$$f{\left(x \right)} = \cot{\left(x \right)} \csc{\left(x \right)}$$$:
$${\color{red}{\int{6 \cot{\left(x \right)} \csc{\left(x \right)} d x}}} = {\color{red}{\left(6 \int{\cot{\left(x \right)} \csc{\left(x \right)} d x}\right)}}$$
De integraal van $$$\cot{\left(x \right)} \csc{\left(x \right)}$$$ is $$$\int{\cot{\left(x \right)} \csc{\left(x \right)} d x} = - \csc{\left(x \right)}$$$:
$$6 {\color{red}{\int{\cot{\left(x \right)} \csc{\left(x \right)} d x}}} = 6 {\color{red}{\left(- \csc{\left(x \right)}\right)}}$$
Dus,
$$\int{6 \cot{\left(x \right)} \csc{\left(x \right)} d x} = - 6 \csc{\left(x \right)}$$
Voeg de integratieconstante toe:
$$\int{6 \cot{\left(x \right)} \csc{\left(x \right)} d x} = - 6 \csc{\left(x \right)}+C$$
Antwoord
$$$\int 6 \cot{\left(x \right)} \csc{\left(x \right)}\, dx = - 6 \csc{\left(x \right)} + C$$$A