integral from 1 to 2 of (x^2)/(x^3-8)

Lösung

\int_{1}^{2} \frac{x ^{2}}{x ^{3} - 8} d x

divergiert

Schritte zur Lösung

\int_{1}^{2} \frac{x ^{2}}{x ^{3} - 8} d x

Wende U-Substitution an

= \int_{- 7}^{0} \frac{1}{3 u} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{- 7}^{0} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{- 7}^{0}

Berechne die Grenzen:

divergiert

= divergiert

\int_{0}^{1} (3 x^{e} + 7 e^{x}) d x

\int_{0}^{e^{2}} ln (x) d x

\int_{0}^{1} \frac{3}{x ^{2} + 1} d x

\int_{2}^{8} 4 x d x

\int_{0}^{8} 6 t^{2} - 2 t + 5 d t