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

Lösung

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

\frac{2}{3} x (x - 3)^{\frac{3}{2}} - \frac{4}{15} (x - 3)^{\frac{5}{2}} + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{2}{3} (x - 3)^{\frac{3}{2}} d x = \frac{4}{15} (x - 3)^{\frac{5}{2}}

= \frac{2}{3} x (x - 3)^{\frac{3}{2}} - \frac{4}{15} (x - 3)^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x (x - 3)^{\frac{3}{2}} - \frac{4}{15} (x - 3)^{\frac{5}{2}} + C

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