integral of (x+5)^{3/2}

Lösung

\int (x + 5)^{\frac{3}{2}} d x

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

Schritte zur Lösung

\int (x + 5)^{\frac{3}{2}} d x

Wende U-Substitution an

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

Wende die Potenzregel an

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

Setze in

u = x + 5

ein

= \frac{2}{5} (x + 5)^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

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

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