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Beliebt Rechnen >

integral of sqrt(x)(sqrt(x)+1)^2

Lösung

\int x (x + 1)^{2} d x

Lösung

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

Schritte zur Lösung

\int x (x + 1)^{2} d x

Multipliziere aus

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

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

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

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

\int 2 x d x = x^{2}

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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