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Beliebt Rechnen >

integral of 4sqrt(x)(x+10)

Lösung

\int 4 x (x + 10) d x

Lösung

4 (\frac{2}{5} x^{\frac{5}{2}} + \frac{20}{3} x^{\frac{3}{2}}) + C

Schritte zur Lösung

\int 4 x (x + 10) d x

Entferne die Konstante:

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

= 4 \cdot \int x (x + 10) d x

Multipliziere aus

x (x + 10) : x^{\frac{3}{2}} + 10 x

= 4 \cdot \int x^{\frac{3}{2}} + 10 x 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

= 4 (\int x^{\frac{3}{2}} d x + \int 10 x d x)

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

\int 10 x d x = \frac{20}{3} x^{\frac{3}{2}}

= 4 (\frac{2}{5} x^{\frac{5}{2}} + \frac{20}{3} x^{\frac{3}{2}})

Füge eine Konstante zur Lösung hinzu

= 4 (\frac{2}{5} x^{\frac{5}{2}} + \frac{20}{3} x^{\frac{3}{2}}) + C

Graph

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