integral of y^2\sqrt[5]{2-4y^3}

Lösung

\int y^{2} 5 2 - 4 y^{3} d y

- \frac{5}{72} (2 - 4 y^{3})^{\frac{6}{5}} + C

Schritte zur Lösung

\int y^{2} 5 2 - 4 y^{3} d y

Wende U-Substitution an

= \int - \frac{5 u}{12} d u

Entferne die Konstante:

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

= - \frac{1}{12} \cdot \int 5 u d u

Wende die Potenzregel an

= - \frac{1}{12} \cdot \frac{5}{6} u^{\frac{6}{5}}

Setze in

u = 2 - 4 y^{3}

ein

= - \frac{1}{12} \cdot \frac{5}{6} (2 - 4 y^{3})^{\frac{6}{5}}

Vereinfache

- \frac{1}{12} \cdot \frac{5}{6} (2 - 4 y^{3})^{\frac{6}{5}} : - \frac{5}{72} (2 - 4 y^{3})^{\frac{6}{5}}

= - \frac{5}{72} (2 - 4 y^{3})^{\frac{6}{5}}

Füge eine Konstante zur Lösung hinzu

= - \frac{5}{72} (2 - 4 y^{3})^{\frac{6}{5}} + C

s l o p e (- \frac{3}{4}, \frac{1}{4}), (\frac{1}{2}, - \frac{3}{2})

a re a f (x) = x^{2} - 4, g (x) = 0, x = - 4, x = 3

\frac{\partial}{\partial y} (25 - x^{2} - 5 y)

\int 6 x 1 + x^{2} d x

y^{^{''}} + 20 y^{^{'}} + 500 y = 0