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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{1}{5} (5 - x^{3})^{\frac{5}{3}} + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int - \frac{u ^{\frac{2}{3}}}{3} d u

Entferne die Konstante:

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

= - \frac{1}{3} \cdot \int u^{\frac{2}{3}} d u

Wende die Potenzregel an

= - \frac{1}{3} \cdot \frac{3}{5} u^{\frac{5}{3}}

Setze in

u = 5 - x^{3}

ein

= - \frac{1}{3} \cdot \frac{3}{5} (5 - x^{3})^{\frac{5}{3}}

Vereinfache

- \frac{1}{3} \cdot \frac{3}{5} (5 - x^{3})^{\frac{5}{3}} : - \frac{1}{5} (5 - x^{3})^{\frac{5}{3}}

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

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} (5 - x^{3})^{\frac{5}{3}} + C

Graph

Beliebte Beispiele

integral of (1-x^3)/((1+x^2)(1-x^2))

\int \frac{1 - x ^{3}}{( 1 + x ^{2} ) ( 1 - x ^{2} )} d x

integral of (x^2-x+5)e^x

\int (x^{2} - x + 5) e^{x} d x

integral of (x+5)/(sqrt(x^2+6x+13))

\int \frac{x + 5}{x ^{2} + 6 x + 13} d x

integral of (e^x+1/(8x))

\int (e^{x} + \frac{1}{8 x}) d x

integral of (xy)/2

\int \frac{x y}{2} d x