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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{7}{3}

+1

Dezimale

2.33333 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Multipliziere aus

x (x^{2} + 1)^{2} : x^{5} + 2 x^{3} + x

= 2 \cdot \int_{0}^{1} x^{5} + 2 x^{3} + x d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int_{0}^{1} x^{5} d x + \int_{0}^{1} 2 x^{3} d x + \int_{0}^{1} x d x)

\int_{0}^{1} x^{5} d x = \frac{1}{6}

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

\int_{0}^{1} x d x = \frac{1}{2}

= 2 (\frac{1}{6} + \frac{1}{2} + \frac{1}{2})

Vereinfache

2 (\frac{1}{6} + \frac{1}{2} + \frac{1}{2}) : \frac{7}{3}

= \frac{7}{3}

Graph

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