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Beliebt Rechnen >

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

Lösung

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

Lösung

- ln ∣ x ∣ + 3 ln ∣ x - 1 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{3}{x - 1} d x = 3 ln ∣ x - 1 ∣

= - ln ∣ x ∣ + 3 ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= - ln ∣ x ∣ + 3 ln ∣ x - 1 ∣ + C

Graph

Beliebte Beispiele

d/(dt)((3y^2-t^2)/(y^5))

\frac{d}{d t} (\frac{3 y ^{2} - t ^{2}}{y ^{5}})

derivative of ln(4/(xsqrt(x+1)))

\frac{d}{d x} (ln (\frac{4}{x x + 1}))

(\partial)/(\partial x)(-2xy)

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

derivative of (x^3-4x+1e^x)

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

limit as x approaches 0 of 5/(tan(3x))

x \to 0 lim (\frac{5}{tan ( 3 x )})