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Beliebt Rechnen >

integral of sqrt(x)(9x^3-2sqrt(x)+8/x)

Lösung

\int x (9 x^{3} - 2 x + \frac{8}{x}) d x

Lösung

16 x + 2 x^{\frac{9}{2}} - x^{2} + C

Schritte zur Lösung

\int x (9 x^{3} - 2 x + \frac{8}{x}) d x

Multipliziere aus

x (9 x^{3} - 2 x + \frac{8}{x}) : \frac{8}{x} + 9 x^{\frac{7}{2}} - 2 x

= \int \frac{8}{x} + 9 x^{\frac{7}{2}} - 2 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{8}{x} d x + \int 9 x^{\frac{7}{2}} d x - \int 2 x d x

\int \frac{8}{x} d x = 16 x

\int 9 x^{\frac{7}{2}} d x = 2 x^{\frac{9}{2}}

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

= 16 x + 2 x^{\frac{9}{2}} - x^{2}

Füge eine Konstante zur Lösung hinzu

= 16 x + 2 x^{\frac{9}{2}} - x^{2} + C

Graph

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