integral from 1 to infinity of 1/(x^e)

Lösung

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

- \frac{1}{- e + 1}

Dezimale

0.58197 \dots

Schritte zur Lösung

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

Berechne das unbestimmte Integral:

\int \frac{1}{x ^{e}} d x = \frac{x ^{- e + 1}}{- e + 1} + C

Berechne die Grenzen:

\int_{1}^{\infty} \frac{1}{x ^{e}} d x = 0 - \frac{1}{- e + 1}

= 0 - \frac{1}{- e + 1}

Vereinfache

= - \frac{1}{- e + 1}

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