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Beliebt Rechnen >

integral of (24)/((x+2)^5)

Lösung

\int \frac{24}{( x + 2 ) ^{5}} d x

Lösung

24 (\frac{x}{( x + 2 ) ^{5}} - \frac{5}{4 ( x + 2 ) ^{4}} + \frac{2}{( x + 2 ) ^{5}}) + C

Schritte zur Lösung

\int \frac{24}{( x + 2 ) ^{5}} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 24 \cdot \int \frac{1}{( x + 2 ) ^{5}} d x

Wende die partielle Integration an

= 24 (\frac{x}{( x + 2 ) ^{5}} - \int - \frac{5 x}{( x + 2 ) ^{6}} d x)

\int - \frac{5 x}{( x + 2 ) ^{6}} d x = \frac{5}{4 ( x + 2 ) ^{4}} - \frac{2}{( x + 2 ) ^{5}}

= 24 (\frac{x}{( x + 2 ) ^{5}} - (\frac{5}{4 ( x + 2 ) ^{4}} - \frac{2}{( x + 2 ) ^{5}}))

Vereinfache

= 24 (\frac{x}{( x + 2 ) ^{5}} - \frac{5}{4 ( x + 2 ) ^{4}} + \frac{2}{( x + 2 ) ^{5}})

Füge eine Konstante zur Lösung hinzu

= 24 (\frac{x}{( x + 2 ) ^{5}} - \frac{5}{4 ( x + 2 ) ^{4}} + \frac{2}{( x + 2 ) ^{5}}) + C

Graph

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