integral of (4x^3+6)ln(x)

Lösung

\int (4 x^{3} + 6) ln (x) d x

x^{4} ln (x) - \frac{x ^{4}}{4} + 6 (x ln (x) - x) + C

Schritte zur Lösung

\int (4 x^{3} + 6) ln (x) d x

Multipliziere aus

(4 x^{3} + 6) ln (x) : 4 x^{3} ln (x) + 6 ln (x)

= \int 4 x^{3} ln (x) + 6 ln (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 4 x^{3} ln (x) d x + \int 6 ln (x) d x

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

\int 6 ln (x) d x = 6 (x ln (x) - x)

= x^{4} ln (x) - \frac{x ^{4}}{4} + 6 (x ln (x) - x)

Füge eine Konstante zur Lösung hinzu

= x^{4} ln (x) - \frac{x ^{4}}{4} + 6 (x ln (x) - x) + C

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