integral from 1 to 9 of 9/((x-1)^{1/3)}

Lösung

\int_{1}^{9} \frac{9}{( x - 1 ) ^{\frac{1}{3}}} d x

54

Schritte zur Lösung

\int_{1}^{9} \frac{9}{( x - 1 ) ^{\frac{1}{3}}} d x

Entferne die Konstante:

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

= 9 \cdot \int_{1}^{9} \frac{1}{( x - 1 ) ^{\frac{1}{3}}} d x

Wende U-Substitution an

= 9 \cdot \int_{0}^{8} \frac{1}{u ^{\frac{1}{3}}} d u

Wende die Potenzregel an

= 9 [\frac{3}{2} u^{\frac{2}{3}}]_{0}^{8}

Berechne die Grenzen:

6

= 9 \cdot 6

Vereinfache

= 54

\int_{1}^{\infty} \frac{1}{n ^{5}}

\int_{4}^{9} \frac{( x + 3 ) ^{2}}{2 x} d x

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\int_{- \frac{1}{2}}^{\frac{1}{2}} x^{2} d x