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Beliebt Rechnen >

integral from 0 to 1 of (x^3+1)/(x+1)

Lösung

\int_{0}^{1} \frac{x ^{3} + 1}{x + 1} d x

Lösung

\frac{5}{6}

+1

Dezimale

0.83333 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{x ^{3} + 1}{x + 1} d x

Vereinfache

\frac{x ^{3} + 1}{x + 1} : x^{2} - x + 1

= \int_{0}^{1} x^{2} - x + 1 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

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

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

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

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

= \frac{1}{3} - \frac{1}{2} + 1

Vereinfache

\frac{1}{3} - \frac{1}{2} + 1 : \frac{5}{6}

= \frac{5}{6}

Graph

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\int (2 x^{\frac{1}{2}}) d x

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\int sin (x) x^{2} d x

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