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Beliebt Rechnen >

integral from 9/8 to 6 of 1/(1-x^2)

Lösung

\int_{\frac{9}{8}}^{6} \frac{1}{1 - x ^{2}} d x

Lösung

\frac{ln ( 7 ) - ln ( 85 )}{2}

+1

Dezimale

- 1.24837 \dots

Schritte zur Lösung

\int_{\frac{9}{8}}^{6} \frac{1}{1 - x ^{2}} d x

Nutze das gemeinsame Integral :

\int \frac{1}{1 - x ^{2}} d x = \frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}

= [\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{\frac{9}{8}}^{6}

Vereinfache

[\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{\frac{9}{8}}^{6} : [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{\frac{9}{8}}^{6}

= [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{\frac{9}{8}}^{6}

Berechne die Grenzen:

\frac{ln ( 7 ) - ln ( 5 ) - ln ( \frac{17}{8} ) - 3 ln ( 2 )}{2}

= \frac{ln ( 7 ) - ln ( 5 ) - ln ( \frac{17}{8} ) - 3 ln ( 2 )}{2}

Vereinfache

= \frac{ln ( 7 ) - ln ( 85 )}{2}

Graph

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