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Integraal van $$$x \tan{\left(3 \right)}$$$
Gerelateerde rekenmachine: Rekenmachine voor bepaalde en oneigenlijke integralen
Uw invoer
Bepaal $$$\int x \tan{\left(3 \right)}\, dx$$$.
Oplossing
Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=\tan{\left(3 \right)}$$$ en $$$f{\left(x \right)} = x$$$:
$${\color{red}{\int{x \tan{\left(3 \right)} d x}}} = {\color{red}{\tan{\left(3 \right)} \int{x d x}}}$$
Pas de machtsregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=1$$$:
$$\tan{\left(3 \right)} {\color{red}{\int{x d x}}}=\tan{\left(3 \right)} {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}=\tan{\left(3 \right)} {\color{red}{\left(\frac{x^{2}}{2}\right)}}$$
Dus,
$$\int{x \tan{\left(3 \right)} d x} = \frac{x^{2} \tan{\left(3 \right)}}{2}$$
Voeg de integratieconstante toe:
$$\int{x \tan{\left(3 \right)} d x} = \frac{x^{2} \tan{\left(3 \right)}}{2}+C$$
Antwoord
$$$\int x \tan{\left(3 \right)}\, dx = \frac{x^{2} \tan{\left(3 \right)}}{2} + C$$$A