integral from 0 to 1/(xy) of ln(y)

Lösung

\int_{0}^{\frac{1}{x y}} ln (y) d y

\frac{- 1 - ln ( x y )}{x y}

Schritte zur Lösung

\int_{0}^{\frac{1}{x y}} ln (y) d y

Wende die partielle Integration an

= [y ln (y) - \int 1 d y]_{0}^{\frac{1}{x y}}

\int 1 d y = y

= [y ln (y) - y]_{0}^{\frac{1}{x y}}

Berechne die Grenzen:

- \frac{1}{x y} - \frac{ln ( x y )}{x y}

= - \frac{1}{x y} - \frac{ln ( x y )}{x y}

Vereinfache

= \frac{- 1 - ln ( x y )}{x y}