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

Lösung

\int_{1}^{\infty} \frac{1}{9 ^{x}} d x

\frac{1}{18 ln ( 3 )}

Dezimale

0.05056 \dots

Schritte zur Lösung

\int_{1}^{\infty} \frac{1}{9 ^{x}} d x

Berechne das unbestimmte Integral:

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

Berechne die Grenzen:

\int_{1}^{\infty} \frac{1}{9 ^{x}} d x = 0 - (- \frac{1}{18 ln ( 3 )})

= 0 - (- \frac{1}{18 ln ( 3 )})

Vereinfache

= \frac{1}{18 ln ( 3 )}

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