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

Lösung

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

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

Dezimale

- 0.15342 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

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

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

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

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

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

Berechne die Grenzen:

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

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

Vereinfache

= - \frac{- ln ( 2 ) - 1}{2} - 1

\frac{\partial}{\partial x} (2 x^{2} + y^{2})

\frac{d}{d x} (- x^{3} + 6 x^{2} - 9 x)

\int \frac{- 5}{x ^{2} + 16} d x

\int \frac{2 e ^{- \frac{6}{x ^{4}}}}{x ^{5}} d x

\frac{d ^{2} y}{d t ^{2}} - 8 \frac{d y}{d t} + 16 y = 0