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Beliebt Rechnen >

integral of 6/(x(x+2))

Lösung

\int \frac{6}{x ( x + 2 )} d x

Lösung

6 (\frac{1}{2} ln ∣ x ∣ - \frac{1}{2} ln ∣ x + 2 ∣) + C

Schritte zur Lösung

\int \frac{6}{x ( x + 2 )} d x

Entferne die Konstante:

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

= 6 \cdot \int \frac{1}{x ( x + 2 )} d x

Ermittle den Partialbruch von

\frac{1}{x ( x + 2 )} : \frac{1}{2 x} - \frac{1}{2 ( x + 2 )}

= 6 \cdot \int \frac{1}{2 x} - \frac{1}{2 ( 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

= 6 (\int \frac{1}{2 x} d x - \int \frac{1}{2 ( x + 2 )} d x)

\int \frac{1}{2 x} d x = \frac{1}{2} ln ∣ x ∣

\int \frac{1}{2 ( x + 2 )} d x = \frac{1}{2} ln ∣ x + 2 ∣

= 6 (\frac{1}{2} ln ∣ x ∣ - \frac{1}{2} ln ∣ x + 2 ∣)

Füge eine Konstante zur Lösung hinzu

= 6 (\frac{1}{2} ln ∣ x ∣ - \frac{1}{2} ln ∣ x + 2 ∣) + C

Graph

Beliebte Beispiele

limit as x approaches 3+of (|x-2|)/(x-2)

x \to 3 + lim (\frac{∣ x - 2 ∣}{x - 2})

(\partial)/(\partial x)(sqrt(56x^2-8y^2-16x-31)+1-8x)

\frac{\partial}{\partial x} (56 x^{2} - 8 y^{2} - 16 x - 31 + 1 - 8 x)

f (x) = 1 + x

integral of 1/(x^{1+c)}

\int \frac{1}{x ^{1 + c}} d x

integral of (-5x^2)/(x^4-1)

\int \frac{- 5 x ^{2}}{x ^{4} - 1} d x