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

Lösung

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

- ln (3) + 2 ln (2)

Dezimale

0.28768 \dots

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

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

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

Vereinfache

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

\int_{0}^{3} (2 - x)^{2} d x

\int_{x^{2}}^{x^{3}} sin (x) d x

\int_{0}^{l n (13)} tanh (x) d x

\int_{0}^{2} \frac{1}{y} d y

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