integral of 4xln(8x^3)

Lösung

\int 4 x ln (8 x^{3}) d x

6 x^{2} ln (2 x) - 3 x^{2} + C

Schritte zur Lösung

\int 4 x ln (8 x^{3}) d x

Entferne die Konstante:

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

= 4 \cdot \int x ln (8 x^{3}) d x

Wende die partielle Integration an

= 4 (\frac{1}{2} x^{2} ln (8 x^{3}) - \int \frac{3 x}{2} d x)

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

= 4 (\frac{1}{2} x^{2} ln (8 x^{3}) - \frac{3 x ^{2}}{4})

Vereinfache

4 (\frac{1}{2} x^{2} ln (8 x^{3}) - \frac{3 x ^{2}}{4}) : 6 x^{2} ln (2 x) - 3 x^{2}

= 6 x^{2} ln (2 x) - 3 x^{2}

Füge eine Konstante zur Lösung hinzu

= 6 x^{2} ln (2 x) - 3 x^{2} + C

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