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Beliebt Rechnen >

integral of sqrt(x)(x+x^{-1})

Lösung

\int x (x + x^{- 1}) d x

Lösung

2 x + \frac{2}{5} x^{\frac{5}{2}} + C

Schritte zur Lösung

\int x (x + x^{- 1}) d x

Wende Exponentenregel an:

a^{- 1} = \frac{1}{a}

= \int x (x + \frac{1}{x}) d x

Multipliziere aus

x (x + \frac{1}{x}) : \frac{1}{x} + x^{\frac{3}{2}}

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

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

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

= 2 x + \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= 2 x + \frac{2}{5} x^{\frac{5}{2}} + C

Graph

Beliebte Beispiele

derivative of 8cos(xsin(x))

\frac{d}{d x} (8 cos (x) sin (x))

y^{^{'}} = y (3 - y)

integral of 3^{x/2}

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

(\partial)/(\partial x)(7yzln(x))

\frac{\partial}{\partial x} (7 yz ln (x))

tangent y= 3/(sqrt(x)),(1,3)

t an g e n t y = \frac{3}{x}, (1, 3)