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Beliebt Rechnen >

integral of ((x-1)/x)^2

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

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