integral of (x^3)^{1/2}

Lösung

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

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

Schritte zur Lösung

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

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

angenommen

x \geq 0

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

Wende die Potenzregel an

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

Füge eine Konstante zur Lösung hinzu

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

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