de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 0 to 5 of x/(sqrt(1+4x))

Lösung

\int_{0}^{5} \frac{x}{1 + 4 x} d x

Lösung

\frac{9 21 + 1}{12}

+1

Dezimale

3.52026 \dots

Schritte zur Lösung

\int_{0}^{5} \frac{x}{1 + 4 x} d x

Wende U-Substitution an

= \int_{1}^{21} \frac{u ^{2} - 1}{8} d u

Entferne die Konstante:

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

= \frac{1}{8} \cdot \int_{1}^{21} u^{2} - 1 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

= \frac{1}{8} (\int_{1}^{21} u^{2} d u - \int_{1}^{21} 1 d u)

\int_{1}^{21} u^{2} d u = 721 - \frac{1}{3}

\int_{1}^{21} 1 d u = 21 - 1

= \frac{1}{8} (721 - \frac{1}{3} - (21 - 1))

Vereinfache

\frac{1}{8} (721 - \frac{1}{3} - (21 - 1)) : \frac{9 21 + 1}{12}

= \frac{9 21 + 1}{12}

Graph

Beliebte Beispiele

integral from 0 to 2 of x-1

\int_{0}^{2} x - 1 d x

x^{''}+2x=0,x(0)=1,x(1)=0

x^{^{''}} + 2 x = 0, x (0) = 1, x (1) = 0

steigung y=x^2-2x-2P(y,x),(2,-2)

s l o p e y = x^{2} - 2 x - 2 P (y, x), (2, - 2)

limit as x approaches 0 of x/(sin(2x))

x \to 0 lim (\frac{x}{sin ( 2 x )})

fläche (2)sin(x),[0,pi]

a re a (2) sin (x), [0, π]