integral of sqrt(x)-1/2 x+2/(sqrt(x))

Lösung

\int x - \frac{1}{2} x + \frac{2}{x} d x

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

Schritte zur Lösung

\int x - \frac{1}{2} 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{1}{2} x d x + \int \frac{2}{x} d x

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

\int \frac{1}{2} x d x = \frac{x ^{2}}{4}

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

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

Füge eine Konstante zur Lösung hinzu

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

\int sec (\frac{1}{2}) x tan (\frac{1}{2}) x d x

\frac{\partial}{\partial x} (2 (\frac{y}{x})^{\frac{1}{2}})

d er i v a t i v e f (x) = 3 x + 3

n = 1 \sum \infty \frac{x ^{n}}{n \cdot 5 n}

\frac{d}{d x} ((x^{3} - 16 x)^{10})