de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of x^3(ln(x))^2

Lösung

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

Lösung

\frac{1}{4} x^{4} ln^{2} (x) - \frac{1}{2} (\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}) + C

Schritte zur Lösung

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

Vereinfache

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

Wende die partielle Integration an

= \frac{1}{4} x^{4} ln^{2} (x) - \int \frac{1}{2} x^{3} ln (x) d x

\int \frac{1}{2} x^{3} ln (x) d x = \frac{1}{2} (\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16})

= \frac{1}{4} x^{4} ln^{2} (x) - \frac{1}{2} (\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} x^{4} ln^{2} (x) - \frac{1}{2} (\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}) + C

Graph

Beliebte Beispiele

inverselaplace s/((s^2+4))

in v erse l a pl a ce \frac{s}{( s ^{2} + 4 )}

limit as x approaches 1 of (x^2-2)^3

x \to 1 lim ((x^{2} - 2)^{3})

derivative f(x)=6sec(x)tan(x)

d er i v a t i v e f (x) = 6 sec (x) tan (x)

integral from 0 to 7 of 1/(sqrt(49+x^2))

\int_{0}^{7} \frac{1}{49 + x ^{2}} d x

integral of 1/(sqrt(4-y^2))

\int \frac{1}{4 - y ^{2}} d y