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Beliebt Rechnen >

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

Lösung

\int \frac{3}{x ^{2} + 4 x - 5} d x

Lösung

3 (\frac{1}{6} ln ∣ x - 1 ∣ - \frac{1}{6} ln ∣ x + 5 ∣) + C

Schritte zur Lösung

\int \frac{3}{x ^{2} + 4 x - 5} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int \frac{1}{x ^{2} + 4 x - 5} d x

Ermittle den Partialbruch von

\frac{1}{x ^{2} + 4 x - 5} : \frac{1}{6 ( x - 1 )} - \frac{1}{6 ( x + 5 )}

= 3 \cdot \int \frac{1}{6 ( x - 1 )} - \frac{1}{6 ( x + 5 )} 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

= 3 (\int \frac{1}{6 ( x - 1 )} d x - \int \frac{1}{6 ( x + 5 )} d x)

\int \frac{1}{6 ( x - 1 )} d x = \frac{1}{6} ln ∣ x - 1 ∣

\int \frac{1}{6 ( x + 5 )} d x = \frac{1}{6} ln ∣ x + 5 ∣

= 3 (\frac{1}{6} ln ∣ x - 1 ∣ - \frac{1}{6} ln ∣ x + 5 ∣)

Füge eine Konstante zur Lösung hinzu

= 3 (\frac{1}{6} ln ∣ x - 1 ∣ - \frac{1}{6} ln ∣ x + 5 ∣) + C

Graph

Beliebte Beispiele

limit as x approaches 0+of (1+x)^{2/x}

derivative f(x)=e^{x^5+2x}

derivative y=x^2y^3+x^3y^2

(dy)/(dx)=e^{(6x-3y)}

derivative of 1/((16-x^2))