integral of (x+3)/(sqrt(x))

Lösung

\int \frac{x + 3}{x} d x

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

Schritte zur Lösung

\int \frac{x + 3}{x} d x

Multipliziere aus

\frac{x + 3}{x} : x + \frac{3}{x}

= \int x + \frac{3}{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{3}{x} d x

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

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

= \frac{2}{3} x^{\frac{3}{2}} + 6 x

Füge eine Konstante zur Lösung hinzu

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

x \to 4 lim (25 - x^{2})

x \to 0 lim ((x + 1)^{2} - x^{2})

\frac{\partial}{\partial x} (x^{8} + x y^{5} + 5)

d er i v a t i v e y = 2 (6 x^{9} - 10 x + 4)^{- 3}

x \to \infty lim (e^{3})