integral of (2/x+x/2)

Lösung

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

2 ln ∣ x ∣ + \frac{x ^{2}}{4} + C

Schritte zur Lösung

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= 2 ln ∣ x ∣ + \frac{x ^{2}}{4}

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x ∣ + \frac{x ^{2}}{4} + C

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

w \to 0 lim (\frac{1 - cos ( 5 w )}{w})

\int_{1}^{2} (4 x^{3} - 6 x) d x

\int_{0}^{x} (2 x - y) d y

\int (1 + 3 x)^{2} d x