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Beliebt Rechnen >

integral of sqrt(x)^5

Lösung

\int x^{5} d x

Lösung

\frac{2}{7} x^{\frac{7}{2}} + C

Schritte zur Lösung

\int (x)^{5} d x

Wende die partielle Integration an

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

\int \frac{5}{2} x^{\frac{5}{2}} d x = \frac{5}{7} x^{\frac{7}{2}}

= x (x)^{5} - \frac{5}{7} x^{\frac{7}{2}}

Vereinfache

x (x)^{5} - \frac{5}{7} x^{\frac{7}{2}} : \frac{2}{7} x^{\frac{7}{2}}

= \frac{2}{7} x^{\frac{7}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{7} x^{\frac{7}{2}} + C

Graph

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