integral of (x^3+1.8x^2-2.4x)

Lösung

\int (x^{3} + 1.8 x^{2} - 2.4 x) d x

0.25 x^{4} + 0.6 x^{3} - 1.2 x^{2} + C

Schritte zur Lösung

\int x^{3} + 1.8 x^{2} - 2.4 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

= \int x^{3} d x + \int 1.8 x^{2} d x - \int 2.4 x d x

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

\int 1.8 x^{2} d x = 0.6 x^{3}

\int 2.4 x d x = 1.2 x^{2}

= \frac{x ^{4}}{4} + 0.6 x^{3} - 1.2 x^{2}

Vereinfache

= 0.25 x^{4} + 0.6 x^{3} - 1.2 x^{2}

Füge eine Konstante zur Lösung hinzu

= 0.25 x^{4} + 0.6 x^{3} - 1.2 x^{2} + C

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