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Beliebt Rechnen >

integral of (6x+6)/((x^2+2x)^2)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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