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Beliebt Rechnen >

integral of (x+2)/(x^3+4x)

Lösung

\int \frac{x + 2}{x ^{3} + 4 x} d x

Lösung

\frac{1}{2} arctan (\frac{x}{2}) + 2 (\frac{1}{4} ln ∣ x ∣ - \frac{1}{8} ln x^{2} + 4) + C

Schritte zur Lösung

\int \frac{x + 2}{x ^{3} + 4 x} d x

Multipliziere aus

\frac{x + 2}{x ^{3} + 4 x} : \frac{x}{x ^{3} + 4 x} + \frac{2}{x ^{3} + 4 x}

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{x}{x ^{3} + 4 x} d x + \int \frac{2}{x ^{3} + 4 x} d x

\int \frac{x}{x ^{3} + 4 x} d x = \frac{1}{2} arctan (\frac{x}{2})

\int \frac{2}{x ^{3} + 4 x} d x = 2 (\frac{1}{4} ln ∣ x ∣ - \frac{1}{8} ln x^{2} + 4)

= \frac{1}{2} arctan (\frac{x}{2}) + 2 (\frac{1}{4} ln ∣ x ∣ - \frac{1}{8} ln x^{2} + 4)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} arctan (\frac{x}{2}) + 2 (\frac{1}{4} ln ∣ x ∣ - \frac{1}{8} ln x^{2} + 4) + C

Graph

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