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Beliebt Rechnen >

integral sqrt(x)(6+5x)

Lösung

integral

x (6 + 5 x)

Lösung

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

Schritte zur Lösung

\int x (6 + 5 x) d x

Multipliziere aus

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

= \int 6 x + 5 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 6 x d x + \int 5 x^{\frac{3}{2}} d x

\int 6 x d x = 4 x^{\frac{3}{2}}

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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