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Beliebt Rechnen >

integral of sqrt(x\sqrt{x\sqrt{x)}}

Lösung

\int x x x d x

Lösung

\frac{8}{15} x^{\frac{15}{8}} + C

Schritte zur Lösung

\int x x x d x

Wende Exponentenregel an:

(a \cdot b)^{n} = a^{n} \cdot b^{n}

x x x = x x x

= \int x x x d x

Wende Exponentenregel an:

(a \cdot b)^{n} = a^{n} \cdot b^{n}

x x = x x

= \int x x x d x

x = 4 x,

angenommen

x \geq 0

= \int x x 4 x d x

Vereinfache

x x 4 x : x^{\frac{7}{8}}

= \int x^{\frac{7}{8}} d x

Wende die Potenzregel an

= \frac{8}{15} x^{\frac{15}{8}}

Füge eine Konstante zur Lösung hinzu

= \frac{8}{15} x^{\frac{15}{8}} + C

Graph

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n = 0 \sum \infty (3 x)^{n}

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