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

Lösung

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

\frac{x ^{2}}{4} - ln ∣ x ∣ + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{x ^{2} - 2}{x} d x

Multipliziere aus

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

= \frac{1}{2} \cdot \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

= \frac{1}{2} (\int x d x - \int \frac{2}{x} d x)

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{1}{2} (\frac{x ^{2}}{2} - 2 ln ∣ x ∣)

Vereinfache

\frac{1}{2} (\frac{x ^{2}}{2} - 2 ln ∣ x ∣) : \frac{x ^{2}}{4} - ln ∣ x ∣

= \frac{x ^{2}}{4} - ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{4} - ln ∣ x ∣ + C

\frac{\partial}{\partial x} (\frac{7 x - 5 y}{y ^{2} + 2 x ^{2}})

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

\frac{\partial}{\partial y} (y arctan (\frac{x}{z}))

d er i v a t i v e h (x) = 4 x^{7}

\int_{2}^{5} \frac{3 x + 3}{x ^{2}} d x