integral from 0 to 1 of (1+2x+x^2)^2

Lösung

\int_{0}^{1} (1 + 2 x + x^{2})^{2} d x

\frac{31}{5}

Dezimale

6.2

Schritte zur Lösung

\int_{0}^{1} (1 + 2 x + x^{2})^{2} d x

Vervollständige das Quadrat

1 + 2 x + x^{2} : (x + 1)^{2}

= \int_{0}^{1} ((x + 1)^{2})^{2} d x

Wende U-Substitution an

= \int_{1}^{2} u^{4} d u

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{31}{5}

= \frac{31}{5}

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