integral from 0 to 1 of 1/(x^2-5x+6)

Lösung

\int_{0}^{1} \frac{1}{x ^{2} - 5 x + 6} d x

2 ln (2) - ln (3)

Dezimale

0.28768 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{1}{x ^{2} - 5 x + 6} d x

Ermittle den Partialbruch von

\frac{1}{x ^{2} - 5 x + 6} : - \frac{1}{x - 2} + \frac{1}{x - 3}

= \int_{0}^{1} - \frac{1}{x - 2} + \frac{1}{x - 3} 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_{0}^{1} \frac{1}{x - 2} d x + \int_{0}^{1} \frac{1}{x - 3} d x

\int_{0}^{1} \frac{1}{x - 2} d x = - ln (2)

\int_{0}^{1} \frac{1}{x - 3} d x = ln (2) - ln (3)

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

Vereinfache

= 2 ln (2) - ln (3)

\int_{0}^{1} x^{3} + \frac{3}{4} d x

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

\int_{0}^{1} (2 x - 1)^{3} d x

\int_{0}^{2} (4 t - 1)^{2} d t

\int_{2}^{3} 6 x d x