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Beliebt Rechnen >

integral of (1/2 x^4+1/4 x^3-x)

Lösung

\int (\frac{1}{2} x^{4} + \frac{1}{4} x^{3} - x) d x

Lösung

\frac{x ^{5}}{10} + \frac{x ^{4}}{16} - \frac{x ^{2}}{2} + C

Schritte zur Lösung

\int \frac{1}{2} x^{4} + \frac{1}{4} x^{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

= \int \frac{1}{2} x^{4} d x + \int \frac{1}{4} x^{3} d x - \int x d x

\int \frac{1}{2} x^{4} d x = \frac{x ^{5}}{10}

\int \frac{1}{4} x^{3} d x = \frac{x ^{4}}{16}

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

= \frac{x ^{5}}{10} + \frac{x ^{4}}{16} - \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{10} + \frac{x ^{4}}{16} - \frac{x ^{2}}{2} + C

Graph

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