integral of (x+2)2

Lösung

\int (x + 2) 2 d x

x^{2} + 4 x + C

Schritte zur Lösung

\int (x + 2) \cdot 2 d x

Entferne die Konstante:

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

= 2 \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

= 2 (\int x d x + \int 2 d x)

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

\int 2 d x = 2 x

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

Vereinfache

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

= x^{2} + 4 x

Füge eine Konstante zur Lösung hinzu

= x^{2} + 4 x + C

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