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 4 of 7(ln(x))/(x^2)

Lösung

\int_{1}^{4} 7 \frac{ln ( x )}{x ^{2}} d x

Lösung

7 (\frac{- 2 ln ( 2 ) - 1}{4} + 1)

+1

Dezimale

2.82398 \dots

Schritte zur Lösung

\int_{1}^{4} 7 \cdot \frac{ln ( x )}{x ^{2}} d x

Entferne die Konstante:

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

= 7 \cdot \int_{1}^{4} \frac{ln ( x )}{x ^{2}} d x

Wende die partielle Integration an

= 7 [- \frac{ln ( x )}{x} - \int - \frac{1}{x ^{2}} d x]_{1}^{4}

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

= 7 [- \frac{ln ( x )}{x} - \frac{1}{x}]_{1}^{4}

Da die Nenner gleich sind, fasse die Brüche zusammen.:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= 7 [\frac{- ln ( x ) - 1}{x}]_{1}^{4}

Berechne die Grenzen:

\frac{- 2 ln ( 2 ) - 1}{4} + 1

= 7 (\frac{- 2 ln ( 2 ) - 1}{4} + 1)

Graph

Beliebte Beispiele

integral of 1/(x+8)

\int \frac{1}{x + 8} d x

integral from 0 to 1 of (2x)/((x^2+5)^2)

\int_{0}^{1} \frac{2 x}{( x ^{2} + 5 ) ^{2}} d x

integral from 0 to pi/4 of (sin(x))^4

\int_{0}^{\frac{π}{4}} (sin (x))^{4} d x

integral of (3u^{-2}-4u^2+1)

\int (3 u^{- 2} - 4 u^{2} + 1) d u

integral of (3x-2)^{20}

\int (3 x - 2)^{20} d x