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Beliebt Rechnen >

integral of 3xe^{(x-2)}+xln(2x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

\int 3 x e^{x - 2} d x = 3 (e^{x - 2} x - e^{x - 2})

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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