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Beliebt Rechnen >

integral of (2+1/x)^2

Lösung

\int (2 + \frac{1}{x})^{2} d x

Lösung

4 x + 4 ln ∣ x ∣ - \frac{1}{x} + C

Schritte zur Lösung

\int (2 + \frac{1}{x})^{2} d x

Wende Exponentenregel an:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{x} = x^{- 1}

= \int (2 + x^{- 1})^{2} d x

Multipliziere aus

(2 + x^{- 1})^{2} : 4 + \frac{4}{x} + \frac{1}{x ^{2}}

= \int 4 + \frac{4}{x} + \frac{1}{x ^{2}} d 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 4 d x + \int \frac{4}{x} d x + \int \frac{1}{x ^{2}} d x

\int 4 d x = 4 x

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int \frac{1}{x ^{2}} d x = - \frac{1}{x}

= 4 x + 4 ln ∣ x ∣ - \frac{1}{x}

Füge eine Konstante zur Lösung hinzu

= 4 x + 4 ln ∣ x ∣ - \frac{1}{x} + C

Graph

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