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Beliebt Rechnen >

integral of sin(x)(cos(x))^{3/2}

Lösung

\int sin (x) (cos (x))^{\frac{3}{2}} d x

Lösung

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

Schritte zur Lösung

\int sin (x) (cos (x))^{\frac{3}{2}} d x

Vereinfache

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Wende die Potenzregel an

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

Setze in

u = cos (x)

ein

= - \frac{2}{5} cos^{\frac{5}{2}} (x)

Füge eine Konstante zur Lösung hinzu

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

Graph

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