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Beliebt Rechnen >

integral from 0 to infinity of 5/(x^2+4)

Lösung

\int_{0}^{\infty} \frac{5}{x ^{2} + 4} d x

Lösung

\frac{5 π}{4}

+1

Dezimale

3.92699 \dots

Schritte zur Lösung

\int_{0}^{\infty} \frac{5}{x ^{2} + 4} d x

Berechne das unbestimmte Integral:

\int \frac{5}{x ^{2} + 4} d x = \frac{5}{2} arctan (\frac{x}{2}) + C

Berechne die Grenzen:

\int_{0}^{\infty} \frac{5}{x ^{2} + 4} d x = \frac{5 π}{4} - 0

= \frac{5 π}{4} - 0

Vereinfache

= \frac{5 π}{4}

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