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

Lösung

\int \frac{( x - 1 )}{x ^{2} + 5 x + 6} d x

- 3 ln ∣ x + 2 ∣ + 4 ln ∣ x + 3 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{x - 1}{x ^{2} + 5 x + 6} : - \frac{3}{x + 2} + \frac{4}{x + 3}

= \int - \frac{3}{x + 2} + \frac{4}{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 \frac{3}{x + 2} d x + \int \frac{4}{x + 3} d x

\int \frac{3}{x + 2} d x = 3 ln ∣ x + 2 ∣

\int \frac{4}{x + 3} d x = 4 ln ∣ x + 3 ∣

= - 3 ln ∣ x + 2 ∣ + 4 ln ∣ x + 3 ∣

Füge eine Konstante zur Lösung hinzu

= - 3 ln ∣ x + 2 ∣ + 4 ln ∣ x + 3 ∣ + C

y^{^{''}} - \frac{5}{t} y^{^{'}} + \frac{25}{t ^{2}} y = 0

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

x \to π lim (tan (\frac{2}{3} x))

d er i v a t i v e f (x) = \frac{x ^{2}}{2 + x}

n \to \infty lim (\frac{n}{1})