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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{4} ln ∣ x + 2 ∣ + \frac{3}{4} ln ∣ x - 2 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

= \int \frac{1}{4 ( x + 2 )} + \frac{3}{4 ( 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

= \int \frac{1}{4 ( x + 2 )} d x + \int \frac{3}{4 ( x - 2 )} d x

\int \frac{1}{4 ( x + 2 )} d x = \frac{1}{4} ln ∣ x + 2 ∣

\int \frac{3}{4 ( x - 2 )} d x = \frac{3}{4} ln ∣ x - 2 ∣

= \frac{1}{4} ln ∣ x + 2 ∣ + \frac{3}{4} ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} ln ∣ x + 2 ∣ + \frac{3}{4} ln ∣ x - 2 ∣ + C

Graph

Beliebte Beispiele

integral of cos(3/x)

\int cos (\frac{3}{x}) d x

integral of (9x)/((x^2+7)^4)

\int \frac{9 x}{( x ^{2} + 7 ) ^{4}} d x

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

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

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

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

integral of ln(sqrt(x+x^2))

\int ln (x + x^{2}) d x