de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 30(x+7)(x+5)^4

Lösung

\int 30 (x + 7) (x + 5)^{4} d x

Lösung

30 (\frac{x ^{6}}{6} + \frac{27 x ^{5}}{5} + \frac{145 x ^{4}}{2} + \frac{1550 x ^{3}}{3} + \frac{4125 x ^{2}}{2} + 4375 x) + C

Schritte zur Lösung

\int 30 (x + 7) (x + 5)^{4} d x

Entferne die Konstante:

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

= 30 \cdot \int (x + 7) (x + 5)^{4} d x

Multipliziere aus

(x + 7) (x + 5)^{4} : x^{5} + 27 x^{4} + 290 x^{3} + 1550 x^{2} + 4125 x + 4375

= 30 \cdot \int x^{5} + 27 x^{4} + 290 x^{3} + 1550 x^{2} + 4125 x + 4375 d x

Wende die Summenregel an:

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

= 30 (\int x^{5} d x + \int 27 x^{4} d x + \int 290 x^{3} d x + \int 1550 x^{2} d x + \int 4125 x d x + \int 4375 d x)

\int x^{5} d x = \frac{x ^{6}}{6}

\int 27 x^{4} d x = \frac{27 x ^{5}}{5}

\int 290 x^{3} d x = \frac{145 x ^{4}}{2}

\int 1550 x^{2} d x = \frac{1550 x ^{3}}{3}

\int 4125 x d x = \frac{4125 x ^{2}}{2}

\int 4375 d x = 4375 x

= 30 (\frac{x ^{6}}{6} + \frac{27 x ^{5}}{5} + \frac{145 x ^{4}}{2} + \frac{1550 x ^{3}}{3} + \frac{4125 x ^{2}}{2} + 4375 x)

Füge eine Konstante zur Lösung hinzu

= 30 (\frac{x ^{6}}{6} + \frac{27 x ^{5}}{5} + \frac{145 x ^{4}}{2} + \frac{1550 x ^{3}}{3} + \frac{4125 x ^{2}}{2} + 4375 x) + C

Graph

Beliebte Beispiele

limit as x approaches 8 of (8x)/(x-8)

x \to 8 lim (\frac{8 x}{x - 8})

y^'=(1-2t)y^2,y(0)=-1/6

y^{^{'}} = (1 - 2 t) y^{2}, y (0) = - \frac{1}{6}

integral of x^3sqrt(x^2+24)

\int x^{3} x^{2} + 24 d x

derivative of (x^2+3/(x+1))

\frac{d}{d x} (\frac{x ^{2} + 3}{x + 1})

integral from 1 to 2 of 5/(2x-1)

\int_{1}^{2} \frac{5}{2 x - 1} d x