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Beliebt Rechnen >

integral of 1/((x^2+3x-4))

Lösung

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

Lösung

\frac{1}{5} ln ∣ x - 1 ∣ - \frac{1}{5} ln ∣ x + 4 ∣ + C

Schritte zur Lösung

\int \frac{1}{x ^{2} + 3 x - 4} d x

Ermittle den Partialbruch von

\frac{1}{x ^{2} + 3 x - 4} : \frac{1}{5 ( x - 1 )} - \frac{1}{5 ( x + 4 )}

= \int \frac{1}{5 ( x - 1 )} - \frac{1}{5 ( 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}{5 ( x - 1 )} d x - \int \frac{1}{5 ( x + 4 )} d x

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

\int \frac{1}{5 ( x + 4 )} d x = \frac{1}{5} ln ∣ x + 4 ∣

= \frac{1}{5} ln ∣ x - 1 ∣ - \frac{1}{5} ln ∣ x + 4 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} ln ∣ x - 1 ∣ - \frac{1}{5} ln ∣ x + 4 ∣ + C

Graph

Beliebte Beispiele

inverselaplace 1/(s^2(s+1))

in v erse l a pl a ce \frac{1}{s ^{2} ( s + 1 )}

integral of (x^3-10x-3)

\int (x^{3} - 10 x - 3) d x

derivative a^3+cos^3(x)

d er i v a t i v e a^{3} + cos^{3} (x)

derivative of ln(1-2x)

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

limit as x approaches infinity of 10

x \to \infty lim (10)