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Beliebt Rechnen >

integral from 0 to 2 of 1/((2-x)^{5/2)}

Lösung

\int_{0}^{2} \frac{1}{( 2 - x ) ^{\frac{5}{2}}} d x

Lösung

divergiert

Schritte zur Lösung

\int_{0}^{2} \frac{1}{( 2 - x ) ^{\frac{5}{2}}} d x

Wende U-Substitution an

= \int_{2}^{0} - \frac{1}{u ^{\frac{5}{2}}} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{2} - \frac{1}{u ^{\frac{5}{2}}} d u

Entferne die Konstante:

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

= - (- \int_{0}^{2} \frac{1}{u ^{\frac{5}{2}}} d u)

Wende die Potenzregel an

= - (- [- \frac{2}{3 u ^{\frac{3}{2}}}]_{0}^{2})

Vereinfache

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

Berechne die Grenzen:

divergiert

= divergiert

Beliebte Beispiele

integral from 2 to 4 of (2x)

\int_{2}^{4} (2 x) d x

integral from-2 to 1 of (2x^3+4x^2-x+3)

\int_{- 2}^{1} (2 x^{3} + 4 x^{2} - x + 3) d x

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

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

integral from 1 to 8 of 1/t

\int_{1}^{8} \frac{1}{t} d t

integral from-3 to 3 of-x^2

\int_{- 3}^{3} - x^{2} d x