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Beliebt Rechnen >

integral of 1/(3x^2-2x-1)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{1}{3 x ^{2} - 2 x - 1} : - \frac{3}{4 ( 3 x + 1 )} + \frac{1}{4 ( x - 1 )}

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 6e^{t/(100)}

\int 6 e^{\frac{t}{100}} d t

integral of x*sqrt(x^9)

\int x \cdot x^{9} d x

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

\int \frac{( x - 1 )}{x ^{2} + 2 x + 5} d x

integral of (2x^4+6x^3-5x^2+2x-3)

\int (2 x^{4} + 6 x^{3} - 5 x^{2} + 2 x - 3) d x

integral of 2(x+1)^{1/2}

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