integral 1/(x-x^2)

Lösung

integral

\frac{1}{x - x ^{2}}

ln ∣ x ∣ - ln ∣ x - 1 ∣ + C

Schritte zur Lösung

\int \frac{1}{x - x ^{2}} d x

Ermittle den Partialbruch von

\frac{1}{x - x ^{2}} : \frac{1}{x} - \frac{1}{x - 1}

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ - ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - ln ∣ x - 1 ∣ + C

in t e g r a l (1 - 4 x) (1 + x)

in t e g r a l 3 - 2 (x)^{- 1}

in t e g r a l \frac{1}{( x )}

in t e g r a l \frac{( 3 x - 13 )}{( x ^{2} - 12 + 45 ) ^{2}}

in t e g r a l \frac{( x + 5 )}{( - 3 x )}