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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{1}{4} (ln x^{2} + 1 - ln x^{2} - 1) - 3 (\frac{1}{6} ln ∣ x + 1 ∣ - \frac{1}{6} ln ∣ x - 1 ∣ - \frac{1}{12} ln ∣ x + 2 ∣ + \frac{1}{12} ln ∣ x - 2 ∣) + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int \frac{x}{x ^{4} - 5 x ^{2} + 4} d x = - \frac{1}{4} (ln x^{2} + 1 - ln x^{2} - 1)

\int \frac{3}{x ^{4} - 5 x ^{2} + 4} d x = 3 (\frac{1}{6} ln ∣ x + 1 ∣ - \frac{1}{6} ln ∣ x - 1 ∣ - \frac{1}{12} ln ∣ x + 2 ∣ + \frac{1}{12} ln ∣ x - 2 ∣)

= - \frac{1}{4} (ln x^{2} + 1 - ln x^{2} - 1) - 3 (\frac{1}{6} ln ∣ x + 1 ∣ - \frac{1}{6} ln ∣ x - 1 ∣ - \frac{1}{12} ln ∣ x + 2 ∣ + \frac{1}{12} ln ∣ x - 2 ∣)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{4} (ln x^{2} + 1 - ln x^{2} - 1) - 3 (\frac{1}{6} ln ∣ x + 1 ∣ - \frac{1}{6} ln ∣ x - 1 ∣ - \frac{1}{12} ln ∣ x + 2 ∣ + \frac{1}{12} ln ∣ x - 2 ∣) + C

Graph

Beliebte Beispiele

integral of (x-56)/(x^2+x-56)

\int \frac{x - 56}{x ^{2} + x - 56} d x

integral of e^{2x}y

\int e^{2 x} y d x

integral of (x^2)/(sqrt(2x-x))

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

integral of (e^x)/(e^{2x)+9e^x+20}

\int \frac{e ^{x}}{e ^{2 x} + 9 e ^{x} + 20} d x

integral of (5e^s)/(1+3e^s)

\int \frac{5 e ^{s}}{1 + 3 e ^{s}} d s