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Beliebt Rechnen >

integral of x^3-3x^2+3x+0.25

Lösung

\int x^{3} - 3 x^{2} + 3 x + 0.25 d x

Lösung

0.25 x^{4} - x^{3} + 1.5 x^{2} + 0.25 x + C

Schritte zur Lösung

\int x^{3} - 3 x^{2} + 3 x + 0.25 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 3 x^{2} d x + \int 3 x d x + \int 0.25 d x

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

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

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

\int 0.25 d x = 0.25 x

= \frac{x ^{4}}{4} - x^{3} + \frac{3 x ^{2}}{2} + 0.25 x

Vereinfache

= 0.25 x^{4} - x^{3} + 1.5 x^{2} + 0.25 x

Füge eine Konstante zur Lösung hinzu

= 0.25 x^{4} - x^{3} + 1.5 x^{2} + 0.25 x + C

Graph

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