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