integral from 1 to 3 of (1+1/u+1/(u^2))

Lösung

\int_{1}^{3} (1 + \frac{1}{u} + \frac{1}{u ^{2}}) d u

ln (3) + \frac{8}{3}

Dezimale

3.76527 \dots

Schritte zur Lösung

\int_{1}^{3} 1 + \frac{1}{u} + \frac{1}{u ^{2}} d u

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}^{3} 1 d u + \int_{1}^{3} \frac{1}{u} d u + \int_{1}^{3} \frac{1}{u ^{2}} d u

\int_{1}^{3} 1 d u = 2

\int_{1}^{3} \frac{1}{u} d u = ln (3)

\int_{1}^{3} \frac{1}{u ^{2}} d u = \frac{2}{3}

= 2 + ln (3) + \frac{2}{3}

Ziehe Brüche zusammen

2 + \frac{2}{3} : \frac{8}{3}

= ln (3) + \frac{8}{3}

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