integral from 8 to infinity of 1/(x^2-9)

Lösung

\int_{8}^{\infty} \frac{1}{x ^{2} - 9} d x

\frac{ln ( \frac{11}{3} ) - ln ( \frac{5}{3} )}{6}

Dezimale

0.13140 \dots

Schritte zur Lösung

\int_{8}^{\infty} \frac{1}{x ^{2} - 9} d x

Berechne das unbestimmte Integral:

\int \frac{1}{x ^{2} - 9} d x = - \frac{1}{6} (ln \frac{x}{3} + 1 - ln \frac{x}{3} - 1) + C

Berechne die Grenzen:

\int_{8}^{\infty} \frac{1}{x ^{2} - 9} d x = 0 - (- \frac{ln ( \frac{11}{3} ) - ln ( \frac{5}{3} )}{6})

= 0 - (- \frac{ln ( \frac{11}{3} ) - ln ( \frac{5}{3} )}{6})

Vereinfache

= \frac{ln ( \frac{11}{3} ) - ln ( \frac{5}{3} )}{6}

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