integral of xln(3x)-x

Lösung

\int x ln (3 x) - x d x

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

Schritte zur Lösung

\int x ln (3 x) - x d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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