integral of (x^2+24x-16)/(x^3-16x)

Lösung

\int \frac{x ^{2} + 24 x - 16}{x ^{3} - 16 x} d x

ln ∣ x ∣ - 3 ln ∣ x + 4 ∣ + 3 ln ∣ x - 4 ∣ + C

Schritte zur Lösung

\int \frac{x ^{2} + 24 x - 16}{x ^{3} - 16 x} d x

Ermittle den Partialbruch von

\frac{x ^{2} + 24 x - 16}{x ^{3} - 16 x} : \frac{1}{x} - \frac{3}{x + 4} + \frac{3}{x - 4}

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{3}{x + 4} d x = 3 ln ∣ x + 4 ∣

\int \frac{3}{x - 4} d x = 3 ln ∣ x - 4 ∣

= ln ∣ x ∣ - 3 ln ∣ x + 4 ∣ + 3 ln ∣ x - 4 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - 3 ln ∣ x + 4 ∣ + 3 ln ∣ x - 4 ∣ + C

d er i v a t i v e \frac{6}{7 t ^{4}}

x \to - 2 lim (\frac{3}{( x + 2 )})

\frac{\partial}{\partial x} (y cos (x y))

x \to 2 + lim (e^{- x})

l a pl a ce t r an s f or m t e^{- t} sin (t)