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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{( x - 1 ) ^{2}}{3 x ^{3}} - \frac{2}{3 x} + \frac{1}{3 x ^{2}} + C

Schritte zur Lösung

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

Vereinfache

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

= \int \frac{( x - 1 ) ^{2}}{x ^{4}} d x

Wende die partielle Integration an

= - \frac{( x - 1 ) ^{2}}{3 x ^{3}} - \int - \frac{2 ( x - 1 )}{3 x ^{3}} d x

\int - \frac{2 ( x - 1 )}{3 x ^{3}} d x = \frac{2}{3 x} - \frac{1}{3 x ^{2}}

= - \frac{( x - 1 ) ^{2}}{3 x ^{3}} - (\frac{2}{3 x} - \frac{1}{3 x ^{2}})

Vereinfache

= - \frac{( x - 1 ) ^{2}}{3 x ^{3}} - \frac{2}{3 x} + \frac{1}{3 x ^{2}}

Füge eine Konstante zur Lösung hinzu

= - \frac{( x - 1 ) ^{2}}{3 x ^{3}} - \frac{2}{3 x} + \frac{1}{3 x ^{2}} + C

Graph

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