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Beliebt Rechnen >

integral of-x^3ln(x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

\int \frac{x ^{3}}{4} d x = \frac{x ^{4}}{16}

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (x^3-x^2-x+3)/(x^2-1)

\int \frac{x ^{3} - x ^{2} - x + 3}{x ^{2} - 1} d x

integral of (x^4+3x^2+3)/(x^2+1)

\int \frac{x ^{4} + 3 x ^{2} + 3}{x ^{2} + 1} d x

integral of (x^2-4x)^5*(4x-8)

\int (x^{2} - 4 x)^{5} \cdot (4 x - 8) d x

integral of pi^2cos(nx)

\int π^{2} cos (n x) d x

integral of (1-x)^{n-1}

\int (1 - x)^{n - 1} d x