integral of sin(x)sqrt(cos(x)-1)

Lösung

\int sin (x) cos (x) - 1 d x

- \frac{2}{3} (cos (x) - 1)^{\frac{3}{2}} + C

Schritte zur Lösung

\int sin (x) cos (x) - 1 d x

Wende U-Substitution an

= \int - u - 1 d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u - 1 d u

Wende U-Substitution an

= - \int v d v

Wende die Potenzregel an

= - \frac{2}{3} v^{\frac{3}{2}}

Ersetze zurück

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

Füge eine Konstante zur Lösung hinzu

= - \frac{2}{3} (cos (x) - 1)^{\frac{3}{2}} + C

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