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(sqrt(x+2))

Lösung

\int ln (x + 2) d x

Lösung

\frac{1}{2} x ln (x + 2) + ln (x + 2) - \frac{1}{2} x - 1 + C

Schritte zur Lösung

\int ln (x + 2) d x

Vereinfache

ln (x + 2) : \frac{1}{2} ln (x + 2)

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

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int ln (x + 2) d x

Wende U-Substitution an

= \frac{1}{2} \cdot \int ln (u) d u

Wende die partielle Integration an

= \frac{1}{2} (u ln (u) - \int 1 d u)

\int 1 d u = u

= \frac{1}{2} (u ln (u) - u)

Setze in

u = x + 2

ein

= \frac{1}{2} ((x + 2) ln (x + 2) - (x + 2))

Vereinfache

\frac{1}{2} ((x + 2) ln (x + 2) - (x + 2)) : \frac{1}{2} x ln (x + 2) + ln (x + 2) - \frac{1}{2} x - 1

= \frac{1}{2} x ln (x + 2) + ln (x + 2) - \frac{1}{2} x - 1

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x ln (x + 2) + ln (x + 2) - \frac{1}{2} x - 1 + C

Graph

Beliebte Beispiele

integral of 7x^3e^x

\int 7 x^{3} e^{x} d x

tangent f(x)=x^2-3x+4,\at x=1

t an g e n t f (x) = x^{2} - 3 x + 4, at x = 1

(dy)/(dt)+2ty=2te^{-t^2}

\frac{d y}{d t} + 2 t y = 2 t e^{- t^{2}}

(\partial)/(\partial z)(xycos(z))

\frac{\partial}{\partial z} (x y cos (z))

integral of x^6-4x^4+x+1

\int x^{6} - 4 x^{4} + x + 1 d x