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Beliebt Rechnen >

integral of 2x(x^2-3)

Lösung

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

Lösung

\frac{x ^{4}}{2} - 3 x^{2} + C

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Multipliziere aus

x (x^{2} - 3) : x^{3} - 3 x

= 2 \cdot \int x^{3} - 3 x 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^{3} d x - \int 3 x d x)

\int x^{3} d x = \frac{x ^{4}}{4}

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

= 2 (\frac{x ^{4}}{4} - \frac{3 x ^{2}}{2})

Vereinfache

2 (\frac{x ^{4}}{4} - \frac{3 x ^{2}}{2}) : \frac{x ^{4}}{2} - 3 x^{2}

= \frac{x ^{4}}{2} - 3 x^{2}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{2} - 3 x^{2} + C

Graph

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