integral of sqrt(x)(x^2-2/x)

Lösung

\int x (x^{2} - \frac{2}{x}) d x

- 4 x + \frac{2}{7} x^{\frac{7}{2}} + C

Schritte zur Lösung

\int x (x^{2} - \frac{2}{x}) d x

Multipliziere aus

x (x^{2} - \frac{2}{x}) : - \frac{2}{x} + x^{\frac{5}{2}}

= \int - \frac{2}{x} + x^{\frac{5}{2}} 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{2}{x} d x + \int x^{\frac{5}{2}} d x

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

\int x^{\frac{5}{2}} d x = \frac{2}{7} x^{\frac{7}{2}}

= - 4 x + \frac{2}{7} x^{\frac{7}{2}}

Füge eine Konstante zur Lösung hinzu

= - 4 x + \frac{2}{7} x^{\frac{7}{2}} + C

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