integral of (6x-15)/(x^2-3x)

Lösung

\int \frac{6 x - 15}{x ^{2} - 3 x} d x

5 ln ∣ x ∣ + ln ∣ x - 3 ∣ + C

Schritte zur Lösung

\int \frac{6 x - 15}{x ^{2} - 3 x} d x

Ermittle den Partialbruch von

\frac{6 x - 15}{x ^{2} - 3 x} : \frac{5}{x} + \frac{1}{x - 3}

= \int \frac{5}{x} + \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 \frac{5}{x} d x + \int \frac{1}{x - 3} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int \frac{1}{x - 3} d x = ln ∣ x - 3 ∣

= 5 ln ∣ x ∣ + ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= 5 ln ∣ x ∣ + ln ∣ x - 3 ∣ + C

\int (2 sin (x) + x) d x

\int \frac{1}{( 7 - 8 x )} d x

n = 1 \sum \infty 99

k = 1 \sum \infty (- \frac{3}{4})^{k - 1}

\frac{d}{d x} (\frac{1}{x} - x)