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Beliebt Rechnen >

integral of (7x-3)/(x^3+2x^2-3x)

Lösung

\int \frac{7 x - 3}{x ^{3} + 2 x ^{2} - 3 x} d x

Lösung

ln ∣ x ∣ + ln ∣ x - 1 ∣ - 2 ln ∣ x + 3 ∣ + C

Schritte zur Lösung

\int \frac{7 x - 3}{x ^{3} + 2 x ^{2} - 3 x} d x

Ermittle den Partialbruch von

\frac{7 x - 3}{x ^{3} + 2 x ^{2} - 3 x} : \frac{1}{x} + \frac{1}{x - 1} - \frac{2}{x + 3}

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

\int \frac{2}{x + 3} d x = 2 ln ∣ x + 3 ∣

= ln ∣ x ∣ + ln ∣ x - 1 ∣ - 2 ln ∣ x + 3 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ + ln ∣ x - 1 ∣ - 2 ln ∣ x + 3 ∣ + C

Graph

Beliebte Beispiele

integral of 3x^4(2x^5+1)^3

\int 3 x^{4} (2 x^{5} + 1)^{3} d x

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

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

integral of (5x)/(sqrt(1+x^4))

\int \frac{5 x}{1 + x ^{4}} d x

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

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

integral of (ln(x+1))/(sqrt(x))

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