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Beliebt Rechnen >

integral of 7x+14xln(3x)

Lösung

\int 7 x + 14 x ln (3 x) d x

Lösung

7 x^{2} ln (3 x) + C

Schritte zur Lösung

\int 7 x + 14 x ln (3 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 7 x d x + \int 14 x ln (3 x) d x

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 14 x ln (3 x) d x = 14 (\frac{1}{2} x^{2} ln (3 x) - \frac{x ^{2}}{4})

= \frac{7 x ^{2}}{2} + 14 (\frac{1}{2} x^{2} ln (3 x) - \frac{x ^{2}}{4})

Vereinfache

\frac{7 x ^{2}}{2} + 14 (\frac{1}{2} x^{2} ln (3 x) - \frac{x ^{2}}{4}) : 7 x^{2} ln (3 x)

= 7 x^{2} ln (3 x)

Füge eine Konstante zur Lösung hinzu

= 7 x^{2} ln (3 x) + C

Graph

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