integral of (sqrt(x))^7

Lösung

\int (x)^{7} d x

\frac{2}{9} x^{\frac{9}{2}} + C

Schritte zur Lösung

\int (x)^{7} d x

Vereinfache

(x)^{7} : (x)^{6} x

= \int (x)^{6} x d x

(x)^{6} = x^{3}

= \int x^{3} x d x

Vereinfache

x^{3} x : x^{\frac{7}{2}}

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

Wende die Potenzregel an

= \frac{2}{9} x^{\frac{9}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{9} x^{\frac{9}{2}} + C

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