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Beliebt Rechnen >

integral of (1/x-1/(x+1))

Lösung

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

Lösung

ln ∣ x ∣ - ln ∣ x + 1 ∣ + C

Schritte zur Lösung

\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

Graph

Beliebte Beispiele

integral of (x+3)/(x-x^3)

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

integral of 7/2 x

\int \frac{7}{2} x d x

integral of-ln(x-2)

\int - ln (x - 2) d x

integral of x^5sqrt(14+x^6)

\int x^{5} 14 + x^{6} d x

integral of 2/(x^2(x+1))

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