de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of sqrt((x^3))ln(\sqrt[3]{x})

Lösung

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

Lösung

\frac{1}{3} (\frac{2}{5} x^{\frac{5}{2}} ln (x) - \frac{4}{25} x^{\frac{5}{2}}) + C

Schritte zur Lösung

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

Vereinfache

x^{3} ln (3 x) : \frac{1}{3} x^{\frac{3}{2}} ln (x)

= \int \frac{1}{3} x^{\frac{3}{2}} ln (x) d x

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int x^{\frac{3}{2}} ln (x) d x

Wende die partielle Integration an

= \frac{1}{3} (\frac{2}{5} x^{\frac{5}{2}} ln (x) - \int \frac{2}{5} x^{\frac{3}{2}} d x)

\int \frac{2}{5} x^{\frac{3}{2}} d x = \frac{4}{25} x^{\frac{5}{2}}

= \frac{1}{3} (\frac{2}{5} x^{\frac{5}{2}} ln (x) - \frac{4}{25} x^{\frac{5}{2}})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} (\frac{2}{5} x^{\frac{5}{2}} ln (x) - \frac{4}{25} x^{\frac{5}{2}}) + C

Graph

Beliebte Beispiele

integral of ((x^3)/(1+x^4))

\int (\frac{x ^{3}}{1 + x ^{4}}) d x

integral of e^{αx}

\int e^{αx} d x

integral of (x^2)/2-x^4+1205/2

\int \frac{x ^{2}}{2} - x^{4} + \frac{1205}{2} d x

integral of 4cos^3(x)sin^2(x)

\int 4 cos^{3} (x) sin^{2} (x) d x

integral of u/(1+u-2u^2)

\int \frac{u}{1 + u - 2 u ^{2}} d u