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Beliebt Rechnen >

integral from 0 to 15 of x/(sqrt(x+1))

Lösung

\int_{0}^{15} \frac{x}{x + 1} d x

Lösung

36

Schritte zur Lösung

\int_{0}^{15} \frac{x}{x + 1} d x

Wende U-Substitution an

= \int_{1}^{4} 2 (u^{2} - 1) d u

Entferne die Konstante:

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

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

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_{1}^{4} u^{2} d u - \int_{1}^{4} 1 d u)

\int_{1}^{4} u^{2} d u = 21

\int_{1}^{4} 1 d u = 3

= 2 (21 - 3)

Vereinfache

= 36

Graph

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