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 e of (ln(x))/(x^2)

Lösung

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

Lösung

- \frac{2}{e} + 1

+1

Dezimale

0.26424 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [\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}

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

x \frac{1}{x} = 1

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

Berechne die Grenzen:

- \frac{2}{e} + 1

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

Graph

Beliebte Beispiele

derivative f(x)=x^8

d er i v a t i v e f (x) = x^{8}

derivative of e^{-x}+x^3-6

\frac{d}{d x} (e^{- x} + x^{3} - 6)

integral of 2*x

\int 2 \cdot x d x

limit as x approaches 0 of (sin(4x))/4

x \to 0 lim (\frac{sin ( 4 x )}{4})

tangent y= 2/(x-2)

t an g e n t y = \frac{2}{x - 2}