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

Lösung

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

\frac{1}{3} (2 ln (5) - ln (6))

Dezimale

0.47570 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{6}^{25} \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_{6}^{25} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{6}^{25}

Berechne die Grenzen:

2 ln (5) - ln (6)

= \frac{1}{3} (2 ln (5) - ln (6))

\int_{- 5}^{3.5} - 2 x^{2} - 3 x + 35 d x

\int_{0}^{3} \frac{x}{1 + 7 x ^{2}} d x

\int_{3}^{6} ln (x) d x

\int_{4}^{7} 4 x d x

\int_{- 1}^{1} - 4 x^{5} + 3 x - 2 d x