integral from 0 to e of (x^2)/(x^3+e)

Lösung

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

\frac{1}{3} (ln (e^{3} + e) - 1)

Dezimale

0.70897 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{e}^{e^{3} + e} \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_{e}^{e^{3} + e} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{e}^{e^{3} + e}

Berechne die Grenzen:

ln (e^{3} + e) - 1

= \frac{1}{3} (ln (e^{3} + e) - 1)

\int_{0}^{\frac{π}{2}} \frac{θ sin ^{2} ( θ )}{2} d θ

\int_{2}^{5} \frac{1}{( 5 x - 20 ) ^{3}} d x

\int_{1}^{3} \frac{3}{20} (x - 3)^{2} d x

\int_{0}^{π} 15 sin^{2} (θ) d θ

\int_{0}^{1} (4 x^{3} - 21 x^{2}) d x