integral of (9x^2+1)ln(x)

Lösung

\int (9 x^{2} + 1) ln (x) d x

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

Schritte zur Lösung

\int (9 x^{2} + 1) ln (x) d x

Multipliziere aus

(9 x^{2} + 1) ln (x) : 9 x^{2} ln (x) + ln (x)

= \int 9 x^{2} ln (x) + 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 9 x^{2} ln (x) d x + \int ln (x) d x

\int 9 x^{2} ln (x) d x = 3 x^{3} ln (x) - x^{3}

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

= 3 x^{3} ln (x) - x^{3} + x ln (x) - x

Füge eine Konstante zur Lösung hinzu

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

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