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Beliebt Rechnen >

integral from 2 to 3 of (x+1)/(x^2-x)

Lösung

\int_{2}^{3} \frac{x + 1}{x ^{2} - x} d x

Lösung

- ln (3) + 3 ln (2)

+1

Dezimale

0.98082 \dots

Schritte zur Lösung

\int_{2}^{3} \frac{x + 1}{x ^{2} - x} d x

Ermittle den Partialbruch von

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

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

\int_{2}^{3} \frac{1}{x} d x = ln (3) - ln (2)

\int_{2}^{3} \frac{2}{x - 1} d x = 2 ln (2)

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

Vereinfache

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

Graph

Beliebte Beispiele

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