integral from 1 to 2 of (9x^2-4x+1)ln(x)

Lösung

\int_{1}^{2} (9 x^{2} - 4 x + 1) ln (x) d x

18 ln (2) - 5

Dezimale

7.47664 \dots

Schritte zur Lösung

\int_{1}^{2} (9 x^{2} - 4 x + 1) ln (x) d x

Multipliziere aus

(9 x^{2} - 4 x + 1) ln (x) : 9 x^{2} ln (x) - 4 x ln (x) + ln (x)

= \int_{1}^{2} 9 x^{2} ln (x) - 4 x 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_{1}^{2} 9 x^{2} ln (x) d x - \int_{1}^{2} 4 x ln (x) d x + \int_{1}^{2} ln (x) d x

\int_{1}^{2} 9 x^{2} ln (x) d x = - 7 + 24 ln (2)

\int_{1}^{2} 4 x ln (x) d x = 8 ln (2) - 3

\int_{1}^{2} ln (x) d x = 2 ln (2) - 1

= - 7 + 24 ln (2) - (8 ln (2) - 3) + 2 ln (2) - 1

Vereinfache

- 7 + 24 ln (2) - (8 ln (2) - 3) + 2 ln (2) - 1 : 18 ln (2) - 5

= 18 ln (2) - 5

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