integral of ((1-x^3))/(x\sqrt[3]{x)}

Lösung

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

- \frac{3}{3 x} - \frac{3}{8} x^{\frac{8}{3}} + C

Schritte zur Lösung

\int \frac{1 - x ^{3}}{x 3 x} d x

Multipliziere aus

\frac{1 - x ^{3}}{x 3 x} : \frac{1}{x 3 x} - x^{\frac{5}{3}}

= \int \frac{1}{x 3 x} - x^{\frac{5}{3}} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{x 3 x} d x - \int x^{\frac{5}{3}} d x

\int \frac{1}{x 3 x} d x = - \frac{3}{3 x}

\int x^{\frac{5}{3}} d x = \frac{3}{8} x^{\frac{8}{3}}

= - \frac{3}{3 x} - \frac{3}{8} x^{\frac{8}{3}}

Füge eine Konstante zur Lösung hinzu

= - \frac{3}{3 x} - \frac{3}{8} x^{\frac{8}{3}} + C

\int a e^{- m x} d x

\frac{d y}{d x} + (\frac{3}{x}) y = - 2 x + 7

x \to - 1 lim (1 + 2 x)

100 y^{^{''}} + 60 y^{^{'}} - 27 y = 0

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