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Beliebt Rechnen >

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

Lösung

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

Lösung

x - 4 ln ∣ x - 1 ∣ + 7 ln ∣ x - 2 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{x ^{2} + 3}{x ^{2} - 3 x + 2} : 1 - \frac{4}{x - 1} + \frac{7}{x - 2}

= \int 1 - \frac{4}{x - 1} + \frac{7}{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 1 d x - \int \frac{4}{x - 1} d x + \int \frac{7}{x - 2} d x

\int 1 d x = x

\int \frac{4}{x - 1} d x = 4 ln ∣ x - 1 ∣

\int \frac{7}{x - 2} d x = 7 ln ∣ x - 2 ∣

= x - 4 ln ∣ x - 1 ∣ + 7 ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= x - 4 ln ∣ x - 1 ∣ + 7 ln ∣ x - 2 ∣ + C

Graph

Beliebte Beispiele

integral of sqrt(x(3x-2))

\int x (3 x - 2) d x

(\partial)/(\partial y)(2x^2)

\frac{\partial}{\partial y} (2 x^{2})

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

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

tangent y=4x^3-2x

t an g e n t y = 4 x^{3} - 2 x

limit as x approaches 5 of x(5)

x \to 5 lim (x (5))