integral from-1 to 2 of 2x(x^2+1)^4

Lösung

\int_{- 1}^{2} 2 x (x^{2} + 1)^{4} d x

\frac{3093}{5}

Dezimale

618.6

Schritte zur Lösung

\int_{- 1}^{2} 2 x (x^{2} + 1)^{4} d x

Entferne die Konstante:

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

= 2 \cdot \int_{- 1}^{2} x (x^{2} + 1)^{4} d x

Wende U-Substitution an

= 2 \cdot \int_{2}^{5} \frac{u ^{4}}{2} d u

Entferne die Konstante:

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

= 2 \cdot \frac{1}{2} \cdot \int_{2}^{5} u^{4} d u

Wende die Potenzregel an

= 2 \cdot \frac{1}{2} [\frac{u ^{5}}{5}]_{2}^{5}

Vereinfache

2 \cdot \frac{1}{2} [\frac{u ^{5}}{5}]_{2}^{5} : [\frac{u ^{5}}{5}]_{2}^{5}

= [\frac{u ^{5}}{5}]_{2}^{5}

Berechne die Grenzen:

\frac{3093}{5}

= \frac{3093}{5}

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