integral from 1 to 2 of (-9ln(x))/(x^2)

Lösung

\int_{1}^{2} \frac{- 9 ln ( x )}{x ^{2}} d x

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

Dezimale

- 1.38083 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{- 9 ln ( x )}{x ^{2}} d x

Entferne die Konstante:

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

= - 9 \cdot \int_{1}^{2} \frac{ln ( x )}{x ^{2}} d x

Wende die partielle Integration an

= - 9 [- \frac{ln ( x )}{x} - \int - \frac{1}{x ^{2}} d x]_{1}^{2}

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

= - 9 [- \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}

= - 9 [\frac{- ln ( x ) - 1}{x}]_{1}^{2}

Berechne die Grenzen:

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

= - 9 (\frac{- ln ( 2 ) - 1}{2} + 1)

\int (\frac{5 x ^{2} + x - 4}{x ^{2}}) d x

x \to 0 lim (x^{\frac{3}{2}})

l a pl a ce t r an s f or m e^{t - 7}

\int 2 + e^{2 t} + e^{- 2 t} d t

d er i v a t i v e x^{2} + 5 x + 9