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Beliebt Rechnen >

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

Lösung

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

Lösung

3 3 x + \frac{2}{5} x^{\frac{5}{2}} + C

Schritte zur Lösung

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

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

angenommen

x \geq 0

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

Multipliziere aus

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

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

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

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

= 3 x^{\frac{1}{3}} + \frac{2}{5} x^{\frac{5}{2}}

Wende Radikal Regel an:

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

= 3 3 x + \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= 3 3 x + \frac{2}{5} x^{\frac{5}{2}} + C

Graph

Beliebte Beispiele

y^{^{'}} = e^{8 x} - 6 x

derivative f(x)=(40t)/(t+2)

d er i v a t i v e f (x) = \frac{40 t}{t + 2}

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h \to 0 lim ((2 x + h) - 2 x)

derivative cos((1-e^{4x})/(1+e^{4x)})

d er i v a t i v e cos (\frac{1 - e ^{4 x}}{1 + e ^{4 x}})

y^{^{'}} = x^{\frac{2}{3}}