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Beliebt Rechnen >

integral of ((2x^4+2\sqrt[5]{x}))/x

Lösung

\int \frac{( 2 x ^{4} + 2 5 x )}{x} d x

Lösung

\frac{x ^{4}}{2} + 10 5 x + C

Schritte zur Lösung

\int \frac{2 x ^{4} + 2 5 x}{x} d x

Multipliziere aus

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

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

= \int 2 x^{3} d x + \int \frac{2}{x ^{\frac{4}{5}}} d x

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int \frac{2}{x ^{\frac{4}{5}}} d x = 10 x^{\frac{1}{5}}

= \frac{x ^{4}}{2} + 10 x^{\frac{1}{5}}

Wende Radikal Regel an:

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

= \frac{x ^{4}}{2} + 10 5 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{2} + 10 5 x + C

Graph

Beliebte Beispiele

limit as t approaches 0 of ((2+t)^3-8)/t

t \to 0 lim (\frac{( 2 + t ) ^{3} - 8}{t})

limit as x approaches-2 of 4x+1

x \to - 2 lim (4 x + 1)

(dy)/(dt)=-5(y-2)

\frac{d y}{d t} = - 5 (y - 2)

t a y l or (x + 1)^{5}

derivative y= 2/3 x^{3/2}

d er i v a t i v e y = \frac{2}{3} x^{\frac{3}{2}}