integral of (y+1)sqrt(1-y)

Lösung

\int (y + 1) 1 - y d y

- \frac{2}{3} (y + 1) (1 - y)^{\frac{3}{2}} - \frac{4}{15} (1 - y)^{\frac{5}{2}} + C

Schritte zur Lösung

\int (y + 1) 1 - y d y

Wende die partielle Integration an

= - \frac{2}{3} (y + 1) (1 - y)^{\frac{3}{2}} - \int - \frac{2}{3} (1 - y)^{\frac{3}{2}} d y

\int - \frac{2}{3} (1 - y)^{\frac{3}{2}} d y = \frac{4}{15} (1 - y)^{\frac{5}{2}}

= - \frac{2}{3} (y + 1) (1 - y)^{\frac{3}{2}} - \frac{4}{15} (1 - y)^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= - \frac{2}{3} (y + 1) (1 - y)^{\frac{3}{2}} - \frac{4}{15} (1 - y)^{\frac{5}{2}} + C

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