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Beliebt Rechnen >

integral from 1 to e of (-2ln(x))/(x^2)

Lösung

\int_{1}^{e} \frac{- 2 ln ( x )}{x ^{2}} d x

Lösung

- 2 (- \frac{2}{e} + 1)

+1

Dezimale

- 0.52848 \dots

Schritte zur Lösung

\int_{1}^{e} \frac{- 2 ln ( x )}{x ^{2}} d x

Entferne die Konstante:

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

= - 2 \cdot \int_{1}^{e} \frac{ln ( x )}{x ^{2}} d x

Wende die partielle Integration an

= - 2 [\frac{- ln ( x ) - x \cdot \int - \frac{1}{x ^{2}} d x}{x}]_{1}^{e}

\int - \frac{1}{x ^{2}} d x = \frac{1}{x}

= - 2 [\frac{- ln ( x ) - x \frac{1}{x}}{x}]_{1}^{e}

x \frac{1}{x} = 1

= - 2 [\frac{- ln ( x ) - 1}{x}]_{1}^{e}

Berechne die Grenzen:

- \frac{2}{e} + 1

= - 2 (- \frac{2}{e} + 1)

Graph

Beliebte Beispiele

integral of x/(1+sin(x))

\int \frac{x}{1 + sin ( x )} d x

tangent f(x)= 1/5 x^{10}-1/3 x^6-x+9

t an g e n t f (x) = \frac{1}{5} x^{10} - \frac{1}{3} x^{6} - x + 9

integral of (2y)/((2+3y^2)^3)

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

(dy)/(dt)=y-y^2

\frac{d y}{d t} = y - y^{2}

limit as x approaches-1 of-x^3+x^2-2

x \to - 1 lim (- x^{3} + x^{2} - 2)