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

Lösung

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

divergiert

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{- 1}^{0} \frac{1}{2 u} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{- 1}^{0} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{- 1}^{0}

Berechne die Grenzen:

divergiert

= divergiert

\int_{0}^{1} x^{7} 1 + 3 x^{8} d x

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

\int_{1}^{64} \frac{1}{x + 3 x} d x

\int_{0}^{1} \frac{e ^{x} + 4}{e ^{x}} d x

\int_{1}^{3} \frac{2 - 6 x}{x ^{3}} d x