de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

\int \frac{x ^{3}}{2} d x = \frac{x ^{4}}{8}

= 2 (\frac{1}{4} x^{4} ln (x^{2}) - \frac{x ^{4}}{8})

Vereinfache

2 (\frac{1}{4} x^{4} ln (x^{2}) - \frac{x ^{4}}{8}) : x^{4} ln (x) - \frac{x ^{4}}{4}

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (8x^9-3x^6+12x^3)

\int (8 x^{9} - 3 x^{6} + 12 x^{3}) d x

integral of (4x^2+x^{-3})

\int (4 x^{2} + x^{- 3}) d x

integral of (x+5)^5

\int (x + 5)^{5} d x

integral of (x+4)^7

\int (x + 4)^{7} d x

integral of x/((x^2+y^2)^{1/2)}

\int \frac{x}{( x ^{2} + y ^{2} ) ^{\frac{1}{2}}} d x