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Beliebt Rechnen >

integral of (2x-4)/(x^2+4)

Lösung

\int \frac{2 x - 4}{x ^{2} + 4} d x

Lösung

ln x^{2} + 4 - 2 arctan (\frac{x}{2}) + C

Schritte zur Lösung

\int \frac{2 x - 4}{x ^{2} + 4} d x

Multipliziere aus

\frac{2 x - 4}{x ^{2} + 4} : \frac{2 x}{x ^{2} + 4} - \frac{4}{x ^{2} + 4}

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{2 x}{x ^{2} + 4} d x - \int \frac{4}{x ^{2} + 4} d x

\int \frac{2 x}{x ^{2} + 4} d x = ln x^{2} + 4

\int \frac{4}{x ^{2} + 4} d x = 2 arctan (\frac{x}{2})

= ln x^{2} + 4 - 2 arctan (\frac{x}{2})

Füge eine Konstante zur Lösung hinzu

= ln x^{2} + 4 - 2 arctan (\frac{x}{2}) + C

Graph

Beliebte Beispiele

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\frac{d}{d x} (x^{2} cos (x y))

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