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

Lösung

\int_{0}^{2} x (x^{2} + 2)^{3} d x

160

Schritte zur Lösung

\int_{0}^{2} x (x^{2} + 2)^{3} d x

Wende U-Substitution an

= \int_{2}^{6} \frac{u ^{3}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{2}^{6} u^{3} d u

Wende die Potenzregel an

= \frac{1}{2} [\frac{u ^{4}}{4}]_{2}^{6}

Berechne die Grenzen:

320

= \frac{1}{2} \cdot 320

Vereinfache

= 160

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