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Beliebt Rechnen >

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

Lösung

\int ln (x + 1) - ln (x) d x

Lösung

x (ln (x + 1) - ln (x)) + ln ∣ x + 1 ∣ + C

Schritte zur Lösung

\int ln (x + 1) - ln (x) d x

Wende die partielle Integration an

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

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

= x (ln (x + 1) - ln (x)) - (- ln ∣ x + 1 ∣)

Vereinfache

= x (ln (x + 1) - ln (x)) + ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= x (ln (x + 1) - ln (x)) + ln ∣ x + 1 ∣ + C

Graph

Beliebte Beispiele

integral of (2+sin(x))/(sqrt(x))

\int \frac{2 + sin ( x )}{x} d x

integral of e^{(-x)/(100)}

\int e^{\frac{- x}{100}} d x

integral of sec^2(1-2x)tan^2(1-2x)

\int sec^{2} (1 - 2 x) tan^{2} (1 - 2 x) d x

integral of sin(ln(x^3))

\int sin (ln (x^{3})) d x

integral of-9/(x^2)

\int - \frac{9}{x ^{2}} d x