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Beliebt Rechnen >

integral of sqrt(x)(x^2-1/x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

x (x^{2} - \frac{1}{x}) : - \frac{1}{x} + x^{\frac{5}{2}}

= \int - \frac{1}{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{1}{x} d x + \int x^{\frac{5}{2}} d x

\int \frac{1}{x} d x = 2 x

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative f(x)=(3x-7)/(5x-2)

d er i v a t i v e f (x) = \frac{3 x - 7}{5 x - 2}

fläche y=20-x,y=sqrt(x),y=1

a re a y = 20 - x, y = x, y = 1

y^{^{''}} + 19 y = 0

integral from 0 to pi/2 of tan^2(x)

\int_{0}^{\frac{π}{2}} tan^{2} (x) d x

(\partial)/(\partial y)(1+x^2)

\frac{\partial}{\partial y} (1 + x^{2})