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

Lösung

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

\frac{1}{3} x^{\frac{3}{2}} + 4 x + C

Schritte zur Lösung

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

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

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

= \frac{1}{3} x^{\frac{3}{2}} + 4 x

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x^{\frac{3}{2}} + 4 x + C

\frac{\partial}{\partial x} (\frac{x + y}{x y - 1})

\frac{d y}{d x} = sin (y) + 1

\frac{d}{d x} (x^{3 c o s (x)})

x \to 8 lim ((1 + 3 x) (x^{3} - 6 x^{2} + 2))

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