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

Lösung

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

\frac{2 arctan ( \frac{2}{2} ) + π}{2 2}

Dezimale

1.54593 \dots

Schritte zur Lösung

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

Berechne das unbestimmte Integral:

\int \frac{1}{x ^{2} + 2} d x = \frac{1}{2} arctan (\frac{x}{2}) + C

Berechne die Grenzen:

\int_{- \infty}^{1} \frac{1}{x ^{2} + 2} d x = \frac{1}{2} arctan (\frac{1}{2}) - (- \frac{π}{2 2})

= \frac{1}{2} arctan (\frac{1}{2}) - (- \frac{π}{2 2})

Vereinfache

= \frac{2 arctan ( \frac{2}{2} ) + π}{2 2}

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