integral of (x-2)/(sqrt(x))

Lösung

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

\frac{2}{3} x^{\frac{3}{2}} - 4 x + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x - 2}{x} : x - \frac{2}{x}

= \int x - \frac{2}{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 x d x - \int \frac{2}{x} d x

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

\int \frac{2}{x} d x = 4 x

= \frac{2}{3} x^{\frac{3}{2}} - 4 x

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x^{\frac{3}{2}} - 4 x + C

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

\frac{\partial}{\partial z} (- y^{2} sin (z))

x \to - 1 + lim ((x + 2 x^{3})^{4})

\int (y^{\frac{3}{2}})^{2} d y

y^{^{''}} + 9 y = 18 - 18 e^{- t}, y (0) = 0, y^{^{'}} (0) = 0