de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of sin^8(x)cos^5(x)

Lösung

\int sin^{8} (x) cos^{5} (x) d x

Lösung

\frac{sin ^{9} ( x )}{9} - \frac{2 sin ^{11} ( x )}{11} + \frac{sin ^{13} ( x )}{13} + C

Schritte zur Lösung

\int sin^{8} (x) cos^{5} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int (1 - sin^{2} (x))^{2} cos (x) sin^{8} (x) d x

Wende U-Substitution an

= \int u^{8} (1 - u^{2})^{2} d u

Multipliziere aus

u^{8} (1 - u^{2})^{2} : u^{8} - 2 u^{10} + u^{12}

= \int u^{8} - 2 u^{10} + u^{12} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{8} d u - \int 2 u^{10} d u + \int u^{12} d u

\int u^{8} d u = \frac{u ^{9}}{9}

\int 2 u^{10} d u = \frac{2 u ^{11}}{11}

\int u^{12} d u = \frac{u ^{13}}{13}

= \frac{u ^{9}}{9} - \frac{2 u ^{11}}{11} + \frac{u ^{13}}{13}

Setze in

u = sin (x)

ein

= \frac{sin ^{9} ( x )}{9} - \frac{2 sin ^{11} ( x )}{11} + \frac{sin ^{13} ( x )}{13}

Füge eine Konstante zur Lösung hinzu

= \frac{sin ^{9} ( x )}{9} - \frac{2 sin ^{11} ( x )}{11} + \frac{sin ^{13} ( x )}{13} + C

Graph

Beliebte Beispiele

derivative of (e^x/(-8x^7))

\frac{d}{d x} (\frac{e ^{x}}{- 8 x ^{7}})

limit as x approaches-infinity of 5x^5-7x^4+1

x \to - \infty lim (5 x^{5} - 7 x^{4} + 1)

xcos^2(y)dx+tan(y)dy=0

x cos^{2} (y) d x + tan (y) d y = 0

slopeintercept (1.1)(0.1)

s l o p e in t erce pt (1.1) (0.1)

derivative of tan(2x^5)

\frac{d}{d x} (tan (2 x^{5}))