integral from 4 to 9 of (2+sqrt(x))/x

Lösung

\int_{4}^{9} \frac{2 + x}{x} d x

2 (2 ln (3) - 2 ln (2)) + 2

Dezimale

3.62186 \dots

Schritte zur Lösung

\int_{4}^{9} \frac{2 + x}{x} d x

Multipliziere aus

\frac{2 + x}{x} : \frac{2}{x} + \frac{1}{x}

= \int_{4}^{9} \frac{2}{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_{4}^{9} \frac{2}{x} d x + \int_{4}^{9} \frac{1}{x} d x

\int_{4}^{9} \frac{2}{x} d x = 2 (2 ln (3) - 2 ln (2))

\int_{4}^{9} \frac{1}{x} d x = 2

= 2 (2 ln (3) - 2 ln (2)) + 2

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