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Beliebt Rechnen >

integral from 0 to 4 of x/(sqrt(1+2x))

Lösung

\int_{0}^{4} \frac{x}{1 + 2 x} d x

Lösung

\frac{10}{3}

+1

Dezimale

3.33333 \dots

Schritte zur Lösung

\int_{0}^{4} \frac{x}{1 + 2 x} d x

Wende U-Substitution an

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

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{1}^{3} 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}{2} (\int_{1}^{3} u^{2} d u - \int_{1}^{3} 1 d u)

\int_{1}^{3} u^{2} d u = \frac{26}{3}

\int_{1}^{3} 1 d u = 2

= \frac{1}{2} (\frac{26}{3} - 2)

Vereinfache

\frac{1}{2} (\frac{26}{3} - 2) : \frac{10}{3}

= \frac{10}{3}

Graph

Beliebte Beispiele

derivative-(2x)/((x^2-1)^2)

d er i v a t i v e - \frac{2 x}{( x ^{2} - 1 ) ^{2}}

derivative of ln(4/x)

\frac{d}{d x} (ln (\frac{4}{x}))

derivative 5/(2x^3)

d er i v a t i v e \frac{5}{2 x ^{3}}

limit as w approaches 0 of (sec(2w)-1)/(wsec(2w))

w \to 0 lim (\frac{sec ( 2 w ) - 1}{w sec ( 2 w )})

fläche y=sqrt(x),y=sqrt(8-x),y=0

a re a y = x, y = 8 - x, y = 0