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Beliebt Rechnen >

integral from 1 to e^2 of (ln(z))/(xz)

Lösung

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

Lösung

\frac{2}{x}

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{1}{x} \cdot \int_{1}^{e^{2}} \frac{ln ( z )}{z} d z

Wende U-Substitution an

= \frac{1}{x} \cdot \int_{0}^{2} u d u

Wende die Potenzregel an

= \frac{1}{x} [\frac{u ^{2}}{2}]_{0}^{2}

Vereinfache

\frac{1}{x} [\frac{u ^{2}}{2}]_{0}^{2} : \frac{[ \frac{u ^{2}}{2} ] _{0}^{2}}{x}

= \frac{[ \frac{u ^{2}}{2} ] _{0}^{2}}{x}

Berechne die Grenzen:

2

= \frac{2}{x}

Beliebte Beispiele

integral from 0 to x of ln(t)

\int_{0}^{x} ln (t) d t

integral from 0 to x of y/x

\int_{0}^{x} \frac{y}{x} d y

integral from 0 to y of cos(10^6t-2y)

\int_{0}^{y} cos (1 0^{6} t - 2 y) d y

integral from 1 to 3 of (1+2x)

\int_{1}^{3} (1 + 2 x) d x

integral from 1 to x of t

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