de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (cos(x))^5sin(x)

Lösung

\int (cos (x))^{5} sin (x) d x

Lösung

- \frac{cos ^{6} ( x )}{6} + C

Schritte zur Lösung

\int (cos (x))^{5} sin (x) d x

Vereinfache

= \int cos^{5} (x) sin (x) d x

Wende U-Substitution an

= \int - u^{5} d u

Entferne die Konstante:

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

= - \int u^{5} d u

Wende die Potenzregel an

= - \frac{u ^{6}}{6}

Setze in

u = cos (x)

ein

= - \frac{cos ^{6} ( x )}{6}

Füge eine Konstante zur Lösung hinzu

= - \frac{cos ^{6} ( x )}{6} + C

Graph

Beliebte Beispiele

integral of (x^2+2x)^5(2x+2)

\int (x^{2} + 2 x)^{5} (2 x + 2) d x

derivative of x^5e^{-x}

\frac{d}{d x} (x^{5} e^{- x})

derivative of (3x+5/(x^2-x))

\frac{d}{d x} (\frac{3 x + 5}{x ^{2} - x})

integral from 0 to 3 of xsqrt(16-x^2)

\int_{0}^{3} x 16 - x^{2} d x

limit as x approaches 0 of-xln(x)-x

x \to 0 lim (- x ln (x) - x)