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Beliebt Rechnen >

integral of xsqrt((x+1)^3)

Lösung

\int x (x + 1)^{3} d x

Lösung

\frac{2}{5} x (x + 1)^{\frac{5}{2}} - \frac{4}{35} (x + 1)^{\frac{7}{2}} + C

Schritte zur Lösung

\int x (x + 1)^{3} d x

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

angenommen

(x + 1) \geq 0

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

Wende die partielle Integration an

= \frac{2}{5} x (x + 1)^{\frac{5}{2}} - \int \frac{2}{5} (x + 1)^{\frac{5}{2}} d x

\int \frac{2}{5} (x + 1)^{\frac{5}{2}} d x = \frac{4}{35} (x + 1)^{\frac{7}{2}}

= \frac{2}{5} x (x + 1)^{\frac{5}{2}} - \frac{4}{35} (x + 1)^{\frac{7}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} x (x + 1)^{\frac{5}{2}} - \frac{4}{35} (x + 1)^{\frac{7}{2}} + C

Graph

Beliebte Beispiele

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