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Beliebt Rechnen >

integral of (x^4+2sqrt(x)-16)

Lösung

\int (x^{4} + 2 x - 16) d x

Lösung

\frac{x ^{5}}{5} + \frac{4}{3} x^{\frac{3}{2}} - 16 x + C

Schritte zur Lösung

\int x^{4} + 2 x - 16 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^{4} d x + \int 2 x d x - \int 16 d x

\int x^{4} d x = \frac{x ^{5}}{5}

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

\int 16 d x = 16 x

= \frac{x ^{5}}{5} + \frac{4}{3} x^{\frac{3}{2}} - 16 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{5} + \frac{4}{3} x^{\frac{3}{2}} - 16 x + C

Graph

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