integral from 1 to 2 of (2x^2+1)/x

Lösung

\int_{1}^{2} \frac{2 x ^{2} + 1}{x} d x

3 + ln (2)

Dezimale

3.69314 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{2 x ^{2} + 1}{x} d x

Multipliziere aus

\frac{2 x ^{2} + 1}{x} : 2 x + \frac{1}{x}

= \int_{1}^{2} 2 x + \frac{1}{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} 2 x d x + \int_{1}^{2} \frac{1}{x} d x

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

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

= 3 + ln (2)

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