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

Lösung

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

divergiert

Schritte zur Lösung

\int_{- 1}^{1} \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}]_{- 1}^{1}

Vereinfache

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

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

Berechne die Grenzen:

divergiert

= divergiert

\int_{50}^{100} \frac{x}{15 + 4 x ^{2}} d x

\int_{- 2}^{3} e^{u + 2} d u

\int_{0}^{3} 9 e^{3 x} d x

\int_{0}^{1} \frac{3}{2} (1 - x^{2}) d x

\int_{0}^{1} e^{- y^{2}} d y