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

Lösung

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

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

Schritte zur Lösung

\int 2 - 3 x + x^{3} 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 2 d x - \int 3 x d x + \int x^{3} d x

\int 2 d x = 2 x

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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