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Beliebt Rechnen >

integral of ((-3x^3+\sqrt[5]{x}))/(5x)

Lösung

\int \frac{( - 3 x ^{3} + 5 x )}{5 x} d x

Lösung

- \frac{1}{5} x^{3} + 5 x + C

Schritte zur Lösung

\int \frac{- 3 x ^{3} + 5 x}{5 x} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int \frac{- 3 x ^{3} + 5 x}{x} d x

Multipliziere aus

\frac{- 3 x ^{3} + 5 x}{x} : - 3 x^{2} + \frac{1}{x ^{\frac{4}{5}}}

= \frac{1}{5} \cdot \int - 3 x^{2} + \frac{1}{x ^{\frac{4}{5}}} 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

= \frac{1}{5} (- \int 3 x^{2} d x + \int \frac{1}{x ^{\frac{4}{5}}} d x)

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

\int \frac{1}{x ^{\frac{4}{5}}} d x = 5 x^{\frac{1}{5}}

= \frac{1}{5} (- x^{3} + 5 x^{\frac{1}{5}})

Vereinfache

\frac{1}{5} (- x^{3} + 5 x^{\frac{1}{5}}) : - \frac{1}{5} x^{3} + 5 x

= - \frac{1}{5} x^{3} + 5 x

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} x^{3} + 5 x + C

Graph

Beliebte Beispiele

derivative of e^{-|x|}

\frac{d}{d x} (e^{- ∣ x ∣})

limit as x approaches-2 of (x+2)/(2x+4)

x \to - 2 lim (\frac{x + 2}{2 x + 4})

integral of 1/((x^2-1)^{3/2)}

\int \frac{1}{( x ^{2} - 1 ) ^{\frac{3}{2}}} d x

fläche y=4x^2-1,y=1-4x^2

a re a y = 4 x^{2} - 1, y = 1 - 4 x^{2}

y^{'} = y (2 - y)