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

Lösung

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

\frac{5}{3}

Dezimale

1.66666 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{4} \frac{u - 1}{1 + u} d u

\frac{u - 1}{1 + u} = u - 1

= \int_{1}^{4} u - 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

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

\int_{1}^{4} u d u = \frac{14}{3}

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

= \frac{14}{3} - 3

Vereinfache

\frac{14}{3} - 3 : \frac{5}{3}

= \frac{5}{3}

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