integral of 1/((x-5)(x-4))

Lösung

\int \frac{1}{( x - 5 ) ( x - 4 )} d x

ln ∣ x - 5 ∣ - ln ∣ x - 4 ∣ + C

Schritte zur Lösung

\int \frac{1}{( x - 5 ) ( x - 4 )} d x

Ermittle den Partialbruch von

\frac{1}{( x - 5 ) ( x - 4 )} : \frac{1}{x - 5} - \frac{1}{x - 4}

= \int \frac{1}{x - 5} - \frac{1}{x - 4} 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{1}{x - 5} d x - \int \frac{1}{x - 4} d x

\int \frac{1}{x - 5} d x = ln ∣ x - 5 ∣

\int \frac{1}{x - 4} d x = ln ∣ x - 4 ∣

= ln ∣ x - 5 ∣ - ln ∣ x - 4 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x - 5 ∣ - ln ∣ x - 4 ∣ + C

\int \frac{y}{( x + y ) ^{2}} d y

\int \frac{tan ( x )}{sin ^{2} ( x )} d x

\int \frac{x + 3}{3 - 2 x - x ^{2}} d x

\int 5 y sin (4 x) d x

\int \frac{2 ( x ^{5} - x ^{3} + 4 )}{x ^{5}} d x