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Integraal van $$$\frac{1}{x^{2} + 1}$$$
Gerelateerde rekenmachine: Rekenmachine voor bepaalde en oneigenlijke integralen
Uw invoer
Bepaal $$$\int \frac{1}{x^{2} + 1}\, dx$$$.
Oplossing
De integraal van $$$\frac{1}{x^{2} + 1}$$$ is $$$\int{\frac{1}{x^{2} + 1} d x} = \operatorname{atan}{\left(x \right)}$$$:
$${\color{red}{\int{\frac{1}{x^{2} + 1} d x}}} = {\color{red}{\operatorname{atan}{\left(x \right)}}}$$
Dus,
$$\int{\frac{1}{x^{2} + 1} d x} = \operatorname{atan}{\left(x \right)}$$
Voeg de integratieconstante toe:
$$\int{\frac{1}{x^{2} + 1} d x} = \operatorname{atan}{\left(x \right)}+C$$
Antwoord
$$$\int \frac{1}{x^{2} + 1}\, dx = \operatorname{atan}{\left(x \right)} + C$$$A
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