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Beliebt Rechnen >

integral of ((x^2+1)/(x^3))^2

Lösung

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

Lösung

- \frac{1}{x} - \frac{2}{3 x ^{3}} - \frac{1}{5 x ^{5}} + C

Schritte zur Lösung

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

Vereinfache

(\frac{x ^{2} + 1}{x ^{3}})^{2} : \frac{( x ^{2} + 1 ) ^{2}}{x ^{6}}

= \int \frac{( x ^{2} + 1 ) ^{2}}{x ^{6}} d x

Multipliziere aus

\frac{( x ^{2} + 1 ) ^{2}}{x ^{6}} : \frac{1}{x ^{2}} + \frac{2}{x ^{4}} + \frac{1}{x ^{6}}

= \int \frac{1}{x ^{2}} + \frac{2}{x ^{4}} + \frac{1}{x ^{6}} 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 \frac{1}{x ^{2}} d x + \int \frac{2}{x ^{4}} d x + \int \frac{1}{x ^{6}} d x

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

\int \frac{2}{x ^{4}} d x = - \frac{2}{3 x ^{3}}

\int \frac{1}{x ^{6}} d x = - \frac{1}{5 x ^{5}}

= - \frac{1}{x} - \frac{2}{3 x ^{3}} - \frac{1}{5 x ^{5}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{x} - \frac{2}{3 x ^{3}} - \frac{1}{5 x ^{5}} + C

Graph

Beliebte Beispiele

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