integral of (x+y)^{1/2}

Lösung

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

\frac{2}{3} (y + x)^{\frac{3}{2}} + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int u^{\frac{1}{2}} d u

Wende die Potenzregel an

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

Setze in

u = y + x

ein

= \frac{2}{3} (y + x)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} (y + x)^{\frac{3}{2}} + C

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