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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{1}{5} ln ∣ x + 1 ∣ + \frac{1}{5} ln ∣ 2 x - 3 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{1}{2 x ^{2} - x - 3} : - \frac{1}{5 ( x + 1 )} + \frac{2}{5 ( 2 x - 3 )}

= \int - \frac{1}{5 ( x + 1 )} + \frac{2}{5 ( 2 x - 3 )} 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}{5 ( x + 1 )} d x + \int \frac{2}{5 ( 2 x - 3 )} d x

\int \frac{1}{5 ( x + 1 )} d x = \frac{1}{5} ln ∣ x + 1 ∣

\int \frac{2}{5 ( 2 x - 3 )} d x = \frac{1}{5} ln ∣ 2 x - 3 ∣

= - \frac{1}{5} ln ∣ x + 1 ∣ + \frac{1}{5} ln ∣ 2 x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} ln ∣ x + 1 ∣ + \frac{1}{5} ln ∣ 2 x - 3 ∣ + C

Graph

Beliebte Beispiele

integral of sin^7(3/5 x)

\int sin^{7} (\frac{3}{5} x) d x

integral of x/(sqrt(x+9))

\int \frac{x}{x + 9} d x

integral of (3^{(2-x)}+(x+1)^2e^{(1-x)})

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

tangent y=3x^2-6,(-1,-3)

t an g e n t y = 3 x^{2} - 6, (- 1, - 3)

integral of 5^{x^2+2x+3}(x+1)

\int 5^{x^{2} + 2 x + 3} (x + 1) d x