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Beliebt Rechnen >

integral from 4/3 to 4 of 1/(1-x^2)

Lösung

\int_{\frac{4}{3}}^{4} \frac{1}{1 - x ^{2}} d x

Lösung

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

+1

Dezimale

- 0.71754 \dots

Schritte zur Lösung

\int_{\frac{4}{3}}^{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{4}{3}}^{4}

Vereinfache

[\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{\frac{4}{3}}^{4} : [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{\frac{4}{3}}^{4}

= [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{\frac{4}{3}}^{4}

Berechne die Grenzen:

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

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

Graph

Beliebte Beispiele

integral of (x^3+1)^2(3x)

\int (x^{3} + 1)^{2} (3 x) d x

tangent y=(sqrt(x))/(x+9),(1,0.1)

t an g e n t y = \frac{x}{x + 9}, (1, 0.1)

tangent-2x^{2/3}-4,\at x=8

t an g e n t - 2 x^{\frac{2}{3}} - 4, at x = 8

derivative (2x^2-4)^3

d er i v a t i v e (2 x^{2} - 4)^{3}

limit as x approaches 0-of (cot(pix)sin(x))/(2sec(x))

x \to 0 - lim (\frac{cot ( π x ) sin ( x )}{2 sec ( x )})