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

Lösung

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

- \frac{3}{7} ln (6)

Dezimale

- 0.76789 \dots

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{x - 1}{x ^{2} - 5 x - 6} : \frac{2}{7 ( x + 1 )} + \frac{5}{7 ( x - 6 )}

= \int_{0}^{5} \frac{2}{7 ( x + 1 )} + \frac{5}{7 ( x - 6 )} 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}^{5} \frac{2}{7 ( x + 1 )} d x + \int_{0}^{5} \frac{5}{7 ( x - 6 )} d x

\int_{0}^{5} \frac{2}{7 ( x + 1 )} d x = \frac{2}{7} ln (6)

\int_{0}^{5} \frac{5}{7 ( x - 6 )} d x = - \frac{5}{7} ln (6)

= \frac{2}{7} ln (6) - \frac{5}{7} ln (6)

Vereinfache

\frac{2}{7} ln (6) - \frac{5}{7} ln (6) : - \frac{3}{7} ln (6)

= - \frac{3}{7} ln (6)

\frac{d}{d x} (\frac{3 x + 36}{2 x + 18})

\int e^{- (x^{2})} d x

x \to \infty + lim (e^{x})

d er i v a t i v e 3 x

h \to 0 lim (\frac{h ^{2} + 2 h}{h})