de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from-1 to 0 of 6(e^{1/x})/(x^3)

Lösung

\int_{- 1}^{0} 6 \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

Lösung

- \frac{12}{e}

+1

Dezimale

- 4.41455 \dots

Schritte zur Lösung

\int_{- 1}^{0} 6 \cdot \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

Entferne die Konstante:

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

= 6 \cdot \int_{- 1}^{0} \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

Wende die partielle Integration an

= 6 [\frac{e ^{\frac{1}{x}}}{x ^{2}} - \int - \frac{e ^{\frac{1}{x}} ( 3 x + 1 )}{x ^{4}} d x]_{- 1}^{0}

\int - \frac{e ^{\frac{1}{x}} ( 3 x + 1 )}{x ^{4}} d x = \frac{3 e ^{\frac{1}{x}}}{x} - e^{\frac{1}{x}} + \frac{e ^{\frac{1}{x}}}{x ^{2}} - \frac{2 e ^{\frac{1}{x}}}{x}

= 6 [\frac{e ^{\frac{1}{x}}}{x ^{2}} - (\frac{3 e ^{\frac{1}{x}}}{x} - e^{\frac{1}{x}} + \frac{e ^{\frac{1}{x}}}{x ^{2}} - \frac{2 e ^{\frac{1}{x}}}{x})]_{- 1}^{0}

Vereinfache

6 [\frac{e ^{\frac{1}{x}}}{x ^{2}} - (\frac{3 e ^{\frac{1}{x}}}{x} - e^{\frac{1}{x}} + \frac{e ^{\frac{1}{x}}}{x ^{2}} - \frac{2 e ^{\frac{1}{x}}}{x})]_{- 1}^{0} : 6 [\frac{- e ^{\frac{1}{x}} + e ^{\frac{1}{x}} x}{x}]_{- 1}^{0}

= 6 [\frac{- e ^{\frac{1}{x}} + e ^{\frac{1}{x}} x}{x}]_{- 1}^{0}

Berechne die Grenzen:

- \frac{2}{e}

= 6 (- \frac{2}{e})

Vereinfache

= - \frac{12}{e}

Graph

Beliebte Beispiele

fläche 12-x-x^2,x+4

a re a 12 - x - x^{2}, x + 4

fläche y1=x^3+4x^2-6x-9,y2=3x^2

a re a y 1 = x^{3} + 4 x^{2} - 6 x - 9, y 2 = 3 x^{2}

tangent f(x)=e^{7x^2},\at x=2

t an g e n t f (x) = e^{7 x^{2}}, at x = 2

integral of y-ye^z

\int y - y e^{z} d x

integral of r/((r^2+x^2)^{3/2)}

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