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Beliebt Rechnen >

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

Lösung

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

Lösung

- arctan (x) - \frac{1}{x} + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

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

= - arctan (x) - \frac{1}{x}

Füge eine Konstante zur Lösung hinzu

= - arctan (x) - \frac{1}{x} + C

Graph

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