integral of y/((y^2-4)^{2/5)}

Lösung

\int \frac{y}{( y ^{2} - 4 ) ^{\frac{2}{5}}} d y

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

Schritte zur Lösung

\int \frac{y}{( y ^{2} - 4 ) ^{\frac{2}{5}}} d y

Wende U-Substitution an

= \int \frac{1}{2 ( u - 4 ) ^{\frac{2}{5}}} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int \frac{1}{( u - 4 ) ^{\frac{2}{5}}} d u

Wende U-Substitution an

= \frac{1}{2} \cdot \int \frac{1}{v ^{\frac{2}{5}}} d v

Wende die Potenzregel an

= \frac{1}{2} \cdot \frac{5}{3} v^{\frac{3}{5}}

Ersetze zurück

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

\int - cos (n x) d x

\frac{d y}{d x} = \frac{x ^{3} + y ^{3}}{x y ^{2}}

\int 4 x + 4 x d x

\int_{0}^{\frac{1}{2}} 8 x - \frac{1}{2} x d x

x \to - 2 lim (x^{5} + 4 x^{3} - 5 x - 2)