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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{e ^{2} - 1}{2} - 1

+1

Dezimale

2.19452 \dots

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{2} - 1}{x} : x - \frac{1}{x}

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

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

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

= \frac{e ^{2} - 1}{2} - 1

Graph

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