integral of (7x-14)/(x^2-3x-10)

Lösung

\int \frac{7 x - 14}{x ^{2} - 3 x - 10} d x

4 ln ∣ x + 2 ∣ + 3 ln ∣ x - 5 ∣ + C

Schritte zur Lösung

\int \frac{7 x - 14}{x ^{2} - 3 x - 10} d x

Ermittle den Partialbruch von

\frac{7 x - 14}{x ^{2} - 3 x - 10} : \frac{4}{x + 2} + \frac{3}{x - 5}

= \int \frac{4}{x + 2} + \frac{3}{x - 5} 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{4}{x + 2} d x + \int \frac{3}{x - 5} d x

\int \frac{4}{x + 2} d x = 4 ln ∣ x + 2 ∣

\int \frac{3}{x - 5} d x = 3 ln ∣ x - 5 ∣

= 4 ln ∣ x + 2 ∣ + 3 ln ∣ x - 5 ∣

Füge eine Konstante zur Lösung hinzu

= 4 ln ∣ x + 2 ∣ + 3 ln ∣ x - 5 ∣ + C

\int \frac{x}{x - 4} d x

\int \frac{1}{( 4 t - 1 ) ln ( 8 t - 2 )} d t

\int 5 x^{3} 9 - x^{2} d x

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\int \frac{13 x ^{14} - 5 x ^{6} + 2 x}{4 x ^{3}} d x