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

Lösung

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

\frac{5}{2}

Dezimale

2.5

Schritte zur Lösung

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

Multipliziere aus

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

= \int_{1}^{2} x + 1 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}^{2} x d x + \int_{1}^{2} 1 d x

\int_{1}^{2} x d x = \frac{3}{2}

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

= \frac{3}{2} + 1

Vereinfache

\frac{3}{2} + 1 : \frac{5}{2}

= \frac{5}{2}

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