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Beliebt Rechnen >

integral from 6/5 to 4 of 1/(1-x^2)

Lösung

\int_{\frac{6}{5}}^{4} \frac{1}{1 - x ^{2}} d x

Lösung

- \frac{ln ( \frac{33}{5} )}{2}

+1

Dezimale

- 0.94353 \dots

Schritte zur Lösung

\int_{\frac{6}{5}}^{4} \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{6}{5}}^{4}

Vereinfache

[\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{\frac{6}{5}}^{4} : [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{\frac{6}{5}}^{4}

= [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{\frac{6}{5}}^{4}

Berechne die Grenzen:

\frac{- ln ( 3 ) - ln ( \frac{11}{5} )}{2}

= \frac{- ln ( 3 ) - ln ( \frac{11}{5} )}{2}

Vereinfache

= - \frac{ln ( \frac{33}{5} )}{2}

Graph

Beliebte Beispiele

integral of x^{3/2}(4-4x)

\int x^{\frac{3}{2}} (4 - 4 x) d x

limit as x approaches infinity of 0.72x

x \to \infty lim (0.72 x)

derivative of 4cos(xsin(x))

\frac{d}{d x} (4 cos (x) sin (x))

derivative f(x)=(x^3+9)/(x^3)

d er i v a t i v e f (x) = \frac{x ^{3} + 9}{x ^{3}}

d/(ds)(s/(s^2+4))

\frac{d}{d s} (\frac{s}{s ^{2} + 4})