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

Lösung

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

\frac{3}{2}

Dezimale

1.5

Schritte zur Lösung

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

Multipliziere aus

\frac{2 - ln ( x )}{x} : \frac{2}{x} - \frac{ln ( x )}{x}

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{1}^{e} \frac{2}{x} d x = 2

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

= 2 - \frac{1}{2}

Vereinfache

2 - \frac{1}{2} : \frac{3}{2}

= \frac{3}{2}

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