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Integraal van $$$717897987691852588770249 x^{50}$$$
Gerelateerde rekenmachine: Rekenmachine voor bepaalde en oneigenlijke integralen
Uw invoer
Bepaal $$$\int 717897987691852588770249 x^{50}\, dx$$$.
Oplossing
Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=717897987691852588770249$$$ en $$$f{\left(x \right)} = x^{50}$$$:
$${\color{red}{\int{717897987691852588770249 x^{50} d x}}} = {\color{red}{\left(717897987691852588770249 \int{x^{50} d x}\right)}}$$
Pas de machtsregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=50$$$:
$$717897987691852588770249 {\color{red}{\int{x^{50} d x}}}=717897987691852588770249 {\color{red}{\frac{x^{1 + 50}}{1 + 50}}}=717897987691852588770249 {\color{red}{\left(\frac{x^{51}}{51}\right)}}$$
Dus,
$$\int{717897987691852588770249 x^{50} d x} = \frac{239299329230617529590083 x^{51}}{17}$$
Voeg de integratieconstante toe:
$$\int{717897987691852588770249 x^{50} d x} = \frac{239299329230617529590083 x^{51}}{17}+C$$
Antwoord
$$$\int 717897987691852588770249 x^{50}\, dx = \frac{239299329230617529590083 x^{51}}{17} + C$$$A