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

Lösung

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

\frac{- 2 ln ( \frac{3}{4} ) + 2 ln ( \frac{5}{4} )}{2}

Dezimale

0.51082 \dots

Schritte zur Lösung

\int_{- \frac{1}{4}}^{\frac{1}{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{1}{4}}^{\frac{1}{4}}

Vereinfache

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

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

Berechne die Grenzen:

\frac{- 2 ln ( \frac{3}{4} ) + 2 ln ( \frac{5}{4} )}{2}

= \frac{- 2 ln ( \frac{3}{4} ) + 2 ln ( \frac{5}{4} )}{2}

l a pl a ce t r an s f or m - 9 t^{2}

\int \frac{3 x}{1 + x ^{2}} d x

\int (- 2 x) d x

\frac{\partial}{\partial x} (x + y^{3})

\frac{\partial}{\partial x} (2 y x - 3 y + y^{2})