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