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Beliebt Rechnen >

integral of 1/((x-1)(x-4))

Lösung

\int \frac{1}{( x - 1 ) ( x - 4 )} d x

Lösung

- \frac{1}{3} ln ∣ x - 1 ∣ + \frac{1}{3} ln ∣ x - 4 ∣ + C

Schritte zur Lösung

\int \frac{1}{( x - 1 ) ( x - 4 )} d x

Ermittle den Partialbruch von

\frac{1}{( x - 1 ) ( x - 4 )} : - \frac{1}{3 ( x - 1 )} + \frac{1}{3 ( x - 4 )}

= \int - \frac{1}{3 ( x - 1 )} + \frac{1}{3 ( x - 4 )} 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{1}{3 ( x - 1 )} d x + \int \frac{1}{3 ( x - 4 )} d x

\int \frac{1}{3 ( x - 1 )} d x = \frac{1}{3} ln ∣ x - 1 ∣

\int \frac{1}{3 ( x - 4 )} d x = \frac{1}{3} ln ∣ x - 4 ∣

= - \frac{1}{3} ln ∣ x - 1 ∣ + \frac{1}{3} ln ∣ x - 4 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{3} ln ∣ x - 1 ∣ + \frac{1}{3} ln ∣ x - 4 ∣ + C

Graph

Beliebte Beispiele

tangent f(x)= 1/(3+2x),\at x=2

t an g e n t f (x) = \frac{1}{3 + 2 x}, at x = 2

integral of (x^2)/(1+x^4)

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

integral of 1/(sqrt(1-9x^2))

\int \frac{1}{1 - 9 x ^{2}} d x

(dy)/(dx)=e^{3x+2y}

\frac{d y}{d x} = e^{3 x + 2 y}

limit as n approaches infinity of n/6 sin(6/n)

n \to \infty lim (\frac{n}{6} sin (\frac{6}{n}))