Reelle Partialbruchzerlegung/X^4+1/Faktorvorgabe/Aufgabe

Bestimme die reelle Partialbruchzerlegung von

{\frac {1}{x^{4}+1}}

unter Verwendung der Zerlegung

{}x^{4}+1={\left(x^{2}+{\sqrt {2}}x+1\right)}{\left(x^{2}-{\sqrt {2}}x+1\right)}\,.

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