integral from 1 to 5 of ((x^2+2)/x)

Lösung

\int_{1}^{5} (\frac{x ^{2} + 2}{x}) d x

12 + 2 ln (5)

Dezimale

15.21887 \dots

Schritte zur Lösung

\int_{1}^{5} \frac{x ^{2} + 2}{x} d x

Multipliziere aus

\frac{x ^{2} + 2}{x} : x + \frac{2}{x}

= \int_{1}^{5} x + \frac{2}{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}^{5} x d x + \int_{1}^{5} \frac{2}{x} d x

\int_{1}^{5} x d x = 12

\int_{1}^{5} \frac{2}{x} d x = 2 ln (5)

= 12 + 2 ln (5)

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