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(3x+1)

Lösung

\int ln (3 x + 1) d x

Lösung

x ln (3 x + 1) + \frac{1}{3} ln (3 x + 1) - x - \frac{1}{3} + C

Schritte zur Lösung

\int ln (3 x + 1) d x

Wende U-Substitution an

= \int ln (u) \frac{1}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int ln (u) d u

Wende die partielle Integration an

= \frac{1}{3} (u ln (u) - \int 1 d u)

\int 1 d u = u

= \frac{1}{3} (u ln (u) - u)

Setze in

u = 3 x + 1

ein

= \frac{1}{3} ((3 x + 1) ln (3 x + 1) - (3 x + 1))

Vereinfache

\frac{1}{3} ((3 x + 1) ln (3 x + 1) - (3 x + 1)) : x ln (3 x + 1) + \frac{1}{3} ln (3 x + 1) - x - \frac{1}{3}

= x ln (3 x + 1) + \frac{1}{3} ln (3 x + 1) - x - \frac{1}{3}

Füge eine Konstante zur Lösung hinzu

= x ln (3 x + 1) + \frac{1}{3} ln (3 x + 1) - x - \frac{1}{3} + C

Graph

Beliebte Beispiele

tangent f(x)=x^3-7x^2

t an g e n t f (x) = x^{3} - 7 x^{2}

(dy)/(dx)=(e^x+10)^2

\frac{d y}{d x} = (e^{x} + 10)^{2}

(\partial}{\partial x}(\frac{(x-y))/z)

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

integral of (sin(x)e^{2x})

\int (sin (x) e^{2 x}) d x

derivative of sin(5/x)

\frac{d}{d x} (sin (\frac{5}{x}))