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

Lösung

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

e^{2}

Dezimale

7.38905 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

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

\int_{1}^{e} \frac{1}{x} d x = 1

= e^{2} - 1 + 1

Vereinfache

= e^{2}

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