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Beliebt Rechnen >

integral from 0 to 5 of xsqrt(1+x)

Lösung

\int_{0}^{5} x 1 + x d x

Lösung

\frac{2}{3} + \frac{72 6 - 2}{5} - 46

+1

Dezimale

25.74135 \dots

Schritte zur Lösung

\int_{0}^{5} x 1 + x d x

Wende U-Substitution an

= \int_{1}^{6} (u - 1) u d u

Multipliziere aus

(u - 1) u : u^{\frac{3}{2}} - u

= \int_{1}^{6} u^{\frac{3}{2}} - u 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}^{6} u^{\frac{3}{2}} d u - \int_{1}^{6} u d u

\int_{1}^{6} u^{\frac{3}{2}} d u = \frac{72 6 - 2}{5}

\int_{1}^{6} u d u = 46 - \frac{2}{3}

= \frac{72 6 - 2}{5} - (46 - \frac{2}{3})

Vereinfache

= \frac{2}{3} + \frac{72 6 - 2}{5} - 46

Graph

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