integral from 1 to e of (14+ln(x))^2

Lösung

\int_{1}^{e} (14 + ln (x))^{2} d x

197 e - 170

Dezimale

365.50152 \dots

Schritte zur Lösung

\int_{1}^{e} (14 + ln (x))^{2} d x

Multipliziere aus

(14 + ln (x))^{2} : 196 + 28 ln (x) + ln^{2} (x)

= \int_{1}^{e} 196 + 28 ln (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_{1}^{e} 196 d x + \int_{1}^{e} 28 ln (x) d x + \int_{1}^{e} ln^{2} (x) d x

\int_{1}^{e} 196 d x = 196 e - 196

\int_{1}^{e} 28 ln (x) d x = 28

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

= 196 e - 196 + 28 + e - 2

Vereinfache

= 197 e - 170

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