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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{x ^{2}}{5} + \frac{4}{5} x + C

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{2}{5} \cdot \int 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

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

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

\int 2 d x = 2 x

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

Vereinfache

\frac{2}{5} (\frac{x ^{2}}{2} + 2 x) : \frac{x ^{2}}{5} + \frac{4}{5} x

= \frac{x ^{2}}{5} + \frac{4}{5} x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{5} + \frac{4}{5} x + C

Graph

Beliebte Beispiele

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