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Integraal van $$$- a^{2} + \frac{1}{a^{2}}$$$ met betrekking tot $$$x$$$
Gerelateerde rekenmachine: Rekenmachine voor bepaalde en oneigenlijke integralen
Uw invoer
Bepaal $$$\int \left(- a^{2} + \frac{1}{a^{2}}\right)\, dx$$$.
Oplossing
Pas de constantenregel $$$\int c\, dx = c x$$$ toe met $$$c=- a^{2} + \frac{1}{a^{2}}$$$:
$${\color{red}{\int{\left(- a^{2} + \frac{1}{a^{2}}\right)d x}}} = {\color{red}{x \left(- a^{2} + \frac{1}{a^{2}}\right)}}$$
Dus,
$$\int{\left(- a^{2} + \frac{1}{a^{2}}\right)d x} = x \left(- a^{2} + \frac{1}{a^{2}}\right)$$
Vereenvoudig:
$$\int{\left(- a^{2} + \frac{1}{a^{2}}\right)d x} = \frac{x \left(1 - a^{4}\right)}{a^{2}}$$
Voeg de integratieconstante toe:
$$\int{\left(- a^{2} + \frac{1}{a^{2}}\right)d x} = \frac{x \left(1 - a^{4}\right)}{a^{2}}+C$$
Antwoord
$$$\int \left(- a^{2} + \frac{1}{a^{2}}\right)\, dx = \frac{x \left(1 - a^{4}\right)}{a^{2}} + C$$$A