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

Lösung

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

- ln ∣ x ∣ - \frac{1}{2} ln ∣ x + 1 ∣ + \frac{3}{2} ln ∣ x - 3 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{5 x + 3}{x ^{3} - 2 x ^{2} - 3 x} : - \frac{1}{x} - \frac{1}{2 ( x + 1 )} + \frac{3}{2 ( x - 3 )}

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{1}{2 ( x + 1 )} d x = \frac{1}{2} ln ∣ x + 1 ∣

\int \frac{3}{2 ( x - 3 )} d x = \frac{3}{2} ln ∣ x - 3 ∣

= - ln ∣ x ∣ - \frac{1}{2} ln ∣ x + 1 ∣ + \frac{3}{2} ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= - ln ∣ x ∣ - \frac{1}{2} ln ∣ x + 1 ∣ + \frac{3}{2} ln ∣ x - 3 ∣ + C

y^{^{'}} = x^{2} \cdot y

\frac{\partial}{\partial x} (ln (x^{6} + y^{3}))

t a y l or sin (x) \frac{π}{4}

\int sec^{2} (11 x) d x

l a pl a ce t r an s f or m e^{- 9 t}