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Beliebt Rechnen >

integral from 1/2 to 5 of 1/((2x-1)^{1/3)}

Lösung

\int_{\frac{1}{2}}^{5} \frac{1}{( 2 x - 1 ) ^{\frac{1}{3}}} d x

Lösung

\frac{3 \cdot 9 ^{\frac{2}{3}}}{4}

+1

Dezimale

3.24506 \dots

Schritte zur Lösung

\int_{\frac{1}{2}}^{5} \frac{1}{( 2 x - 1 ) ^{\frac{1}{3}}} d x

Wende Exponentenregel an:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{( 2 x - 1 ) ^{\frac{1}{3}}} = (2 x - 1)^{- \frac{1}{3}}

= \int_{\frac{1}{2}}^{5} (2 x - 1)^{- \frac{1}{3}} d x

Wende U-Substitution an

= \int_{0}^{9} \frac{1}{2 u ^{\frac{1}{3}}} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{9} \frac{1}{u ^{\frac{1}{3}}} d u

Wende die Potenzregel an

= \frac{1}{2} [\frac{3}{2} u^{\frac{2}{3}}]_{0}^{9}

Berechne die Grenzen:

9^{\frac{2}{3}} \cdot \frac{3}{2}

= \frac{1}{2} \cdot 9^{\frac{2}{3}} \cdot \frac{3}{2}

Vereinfache

= \frac{3 \cdot 9 ^{\frac{2}{3}}}{4}

Graph

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