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

Lösung

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

\frac{3}{2} x^{\frac{2}{3}} - \frac{6}{7} x^{\frac{7}{6}} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{1 - x}{3 x} : \frac{1}{3 x} - 6 x

= \int \frac{1}{3 x} - 6 x 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}{3 x} d x - \int 6 x d x

\int \frac{1}{3 x} d x = \frac{3}{2} x^{\frac{2}{3}}

\int 6 x d x = \frac{6}{7} x^{\frac{7}{6}}

= \frac{3}{2} x^{\frac{2}{3}} - \frac{6}{7} x^{\frac{7}{6}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} x^{\frac{2}{3}} - \frac{6}{7} x^{\frac{7}{6}} + C

x \to - 2 lim (x)

\int \frac{x ^{2} + 1}{( x - 9 ) ( x - 8 ) ^{2}} d x

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

\int_{- 8}^{18} \frac{1}{∣ 2 x ∣} d x

\frac{\partial}{\partial y} (3 y^{2} + x^{2} - 3)