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Beliebt Rechnen >

integral of 2x^{2/3}(1+3/2 x^{5/6})

Lösung

\int 2 x^{\frac{2}{3}} (1 + \frac{3}{2} x^{\frac{5}{6}}) d x

Lösung

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

Schritte zur Lösung

\int 2 x^{\frac{2}{3}} (1 + \frac{3}{2} x^{\frac{5}{6}}) d x

Entferne die Konstante:

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

= 2 \cdot \int x^{\frac{2}{3}} (1 + \frac{3}{2} x^{\frac{5}{6}}) d x

Multipliziere aus

x^{\frac{2}{3}} (1 + \frac{3}{2} x^{\frac{5}{6}}) : x^{\frac{2}{3}} + \frac{3 x ^{\frac{3}{2}}}{2}

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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