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Integraal van $$$\frac{13 x^{2} \cos{\left(1 \right)}}{2}$$$
Gerelateerde rekenmachine: Rekenmachine voor bepaalde en oneigenlijke integralen
Uw invoer
Bepaal $$$\int \frac{13 x^{2} \cos{\left(1 \right)}}{2}\, dx$$$.
Oplossing
Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=\frac{13 \cos{\left(1 \right)}}{2}$$$ en $$$f{\left(x \right)} = x^{2}$$$:
$${\color{red}{\int{\frac{13 x^{2} \cos{\left(1 \right)}}{2} d x}}} = {\color{red}{\left(\frac{13 \cos{\left(1 \right)} \int{x^{2} d x}}{2}\right)}}$$
Pas de machtsregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=2$$$:
$$\frac{13 \cos{\left(1 \right)} {\color{red}{\int{x^{2} d x}}}}{2}=\frac{13 \cos{\left(1 \right)} {\color{red}{\frac{x^{1 + 2}}{1 + 2}}}}{2}=\frac{13 \cos{\left(1 \right)} {\color{red}{\left(\frac{x^{3}}{3}\right)}}}{2}$$
Dus,
$$\int{\frac{13 x^{2} \cos{\left(1 \right)}}{2} d x} = \frac{13 x^{3} \cos{\left(1 \right)}}{6}$$
Voeg de integratieconstante toe:
$$\int{\frac{13 x^{2} \cos{\left(1 \right)}}{2} d x} = \frac{13 x^{3} \cos{\left(1 \right)}}{6}+C$$
Antwoord
$$$\int \frac{13 x^{2} \cos{\left(1 \right)}}{2}\, dx = \frac{13 x^{3} \cos{\left(1 \right)}}{6} + C$$$A