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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{ln ( \frac{9}{4} )}{2}

+1

Dezimale

0.40546 \dots

Schritte zur Lösung

\int_{- \frac{1}{5}}^{\frac{1}{5}} \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{1}{5}}^{\frac{1}{5}}

Vereinfache

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

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

Berechne die Grenzen:

\frac{- 2 ln ( \frac{4}{5} ) + 2 ln ( \frac{6}{5} )}{2}

= \frac{- 2 ln ( \frac{4}{5} ) + 2 ln ( \frac{6}{5} )}{2}

Vereinfache

= \frac{ln ( \frac{9}{4} )}{2}

Graph

Beliebte Beispiele

limit as x approaches 4-of sqrt(x-4)

x \to 4 - lim (x - 4)

derivative t^9cos(t)

d er i v a t i v e t^{9} cos (t)

integral of (ln(x)sin(ln(x)))/x

\int \frac{ln ( x ) sin ( ln ( x ) )}{x} d x

derivative tcos(t)

d er i v a t i v e t cos (t)

fläche y=sqrt(4x),x=4,x=9

a re a y = 4 x, x = 4, x = 9