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Beliebt Rechnen >

integral of 3xln(3x)

Lösung

\int 3 x ln (3 x) d x

Lösung

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

Schritte zur Lösung

\int 3 x ln (3 x) d x

Entferne die Konstante:

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

= 3 \cdot \int x ln (3 x) d x

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

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

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

integral of 4tan(3/2 x)

\int 4 tan (\frac{3}{2} x) d x

derivative of 3^x+x^3

\frac{d}{d x} (3^{x} + x^{3})

integral of ((5x^{(2)}))/((2x^{(3))+1)}

\int \frac{( 5 x ^{(2)} )}{( 2 x ^{(3)} + 1 )} d x

integral from e to infinity of x^eln(x)

\int_{e}^{\infty} x^{e} ln (x) d x