de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of x(1-x)^{10}

Lösung

\int x (1 - x)^{10} d x

Lösung

\frac{1}{12} (1 - x)^{12} - \frac{1}{11} (1 - x)^{11} + C

Schritte zur Lösung

\int x (1 - x)^{10} d x

Wende U-Substitution an

= \int - (- u + 1) u^{10} d u

Entferne die Konstante:

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

= - \int (- u + 1) u^{10} d u

Multipliziere aus

(- u + 1) u^{10} : - u^{11} + u^{10}

= - \int - u^{11} + u^{10} 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^{11} d u + \int u^{10} d u)

\int u^{11} d u = \frac{u ^{12}}{12}

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

= - (- \frac{u ^{12}}{12} + \frac{u ^{11}}{11})

Setze in

u = 1 - x

ein

= - (- \frac{( 1 - x ) ^{12}}{12} + \frac{( 1 - x ) ^{11}}{11})

Vereinfache

- (- \frac{( 1 - x ) ^{12}}{12} + \frac{( 1 - x ) ^{11}}{11}) : \frac{1}{12} (1 - x)^{12} - \frac{1}{11} (1 - x)^{11}

= \frac{1}{12} (1 - x)^{12} - \frac{1}{11} (1 - x)^{11}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{12} (1 - x)^{12} - \frac{1}{11} (1 - x)^{11} + C

Graph

Beliebte Beispiele

t(dQ)/(dt)+Q=t^5ln(t)

t \frac{d Q}{d t} + Q = t^{5} ln (t)

integral of 3/(1+2e^x-e^{-x)}

\int \frac{3}{1 + 2 e ^{x} - e ^{- x}} d x

integral of ((xe^x))/((1+x)^2)

\int \frac{( x e ^{x} )}{( 1 + x ) ^{2}} d x

integral of (x+1)sqrt(6-x)

\int (x + 1) 6 - x d x

limit as x approaches-3-of sqrt(x^3+27)

x \to - 3 - lim (x^{3} + 27)