integral from 0 to x of 1/((1-x^2))

Lösung

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

\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)

Schritte zur Lösung

\int_{0}^{x} \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}]_{0}^{x}

Vereinfache

[\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{0}^{x} : [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{0}^{x}

= [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{0}^{x}

Berechne die Grenzen:

\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)

= \frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)

\int_{- 1}^{2} (4 - x^{2}) - (- x + 2) d x

\int_{1}^{10} \frac{1}{x I n ^{2} x} d x

\int_{1}^{4} x ln (2) d x

\int_{6}^{0} x^{3} d x

\int_{2}^{5} t^{3} ln (4 t) d t