de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of-ln(x+1)

Lösung

\int - ln (x + 1) d x

Lösung

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

Schritte zur Lösung

\int - ln (x + 1) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Wende U-Substitution an

= - \int ln (u) d u

Wende die partielle Integration an

= - (u ln (u) - \int 1 d u)

\int 1 d u = u

= - (u ln (u) - u)

Setze in

u = x + 1

ein

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

Vereinfache

- ((x + 1) ln (x + 1) - (x + 1)) : - x ln (x + 1) - ln (x + 1) + x + 1

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of b/(cos(θ))

\frac{d}{d x} (\frac{b}{cos ( θ )})

integral of+17cot^4(x)

\int + 17 cot^{4} (x) d x

(3dy)/(dx)+15y=90,y(0)=0

\frac{3 d y}{d x} + 15 y = 90, y (0) = 0

integral of (2sin(x)-pi/4 x)

\int (2 sin (x) - \frac{π}{4} x) d x

derivative of ln(x/x)

\frac{d}{d x} (ln (\frac{x}{x}))