integral from 1 to e of (1+sqrt(x))/x

Lösung

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

2 e - 1

Dezimale

2.29744 \dots

Schritte zur Lösung

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

Multipliziere aus

\frac{1 + x}{x} : \frac{1}{x} + \frac{1}{x}

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

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

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

= 1 + 2 e - 2

Vereinfache

= 2 e - 1

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