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Beliebt Rechnen >

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

Lösung

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

Lösung

2 (ln ∣ x - 2 ∣ - ln ∣ x - 1 ∣) + C

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Ermittle den Partialbruch von

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

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

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

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

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

= 2 (ln ∣ x - 2 ∣ - ln ∣ x - 1 ∣)

Füge eine Konstante zur Lösung hinzu

= 2 (ln ∣ x - 2 ∣ - ln ∣ x - 1 ∣) + C

Graph

Beliebte Beispiele

integral of (sqrt(4-x^2))/(x^3)

\int \frac{4 - x ^{2}}{x ^{3}} d x

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

integral of x^24^{-x}

\int x^{2} 4^{- x} d x

integral of (2/x+1)^2

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

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\int a^{n y} d y