integral of 4xln(2x)

Lösung

\int 4 x ln (2 x) d x

2 x^{2} ln (2 x) - x^{2} + C

Schritte zur Lösung

\int 4 x ln (2 x) d x

Entferne die Konstante:

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

= 4 \cdot \int x ln (2 x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

= 2 x^{2} ln (2 x) - x^{2}

Füge eine Konstante zur Lösung hinzu

= 2 x^{2} ln (2 x) - x^{2} + C

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