integral from 1 to 2 of-(5ln(x))/(x^2)

Lösung

\int_{1}^{2} - \frac{5 ln ( x )}{x ^{2}} d x

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

Dezimale

- 0.76713 \dots

Schritte zur Lösung

\int_{1}^{2} - \frac{5 ln ( x )}{x ^{2}} d x

Entferne die Konstante:

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

= - 5 \cdot \int_{1}^{2} \frac{ln ( x )}{x ^{2}} d x

Wende die partielle Integration an

= - 5 [- \frac{ln ( x )}{x} - \int - \frac{1}{x ^{2}} d x]_{1}^{2}

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

= - 5 [- \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}

= - 5 [\frac{- ln ( x ) - 1}{x}]_{1}^{2}

Berechne die Grenzen:

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

= - 5 (\frac{- ln ( 2 ) - 1}{2} + 1)

\int \frac{- 5}{x} d x

\int x^{- 6} (x + 1) d x

y^{^{''}} - 9 y^{^{'}} + 18 y = 2 sin (5 t)

t a y l or e^{c o s (s i n (x^{2}))}

\int_{- 1}^{1} - 1 d x