integral of (82x+8)/((9x+1)(x-1))

Lösung

\int \frac{82 x + 8}{( 9 x + 1 ) ( x - 1 )} d x

\frac{1}{9} ln ∣ 9 x + 1 ∣ + 9 ln ∣ x - 1 ∣ + C

Schritte zur Lösung

\int \frac{82 x + 8}{( 9 x + 1 ) ( x - 1 )} d x

Ermittle den Partialbruch von

\frac{82 x + 8}{( 9 x + 1 ) ( x - 1 )} : \frac{1}{9 x + 1} + \frac{9}{x - 1}

= \int \frac{1}{9 x + 1} + \frac{9}{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}{9 x + 1} d x + \int \frac{9}{x - 1} d x

\int \frac{1}{9 x + 1} d x = \frac{1}{9} ln ∣ 9 x + 1 ∣

\int \frac{9}{x - 1} d x = 9 ln ∣ x - 1 ∣

= \frac{1}{9} ln ∣ 9 x + 1 ∣ + 9 ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{9} ln ∣ 9 x + 1 ∣ + 9 ln ∣ x - 1 ∣ + C

9 (t + 1) (\frac{d y}{d t}) - 6 y = 18 t

d er i v a t i v e \frac{17}{x}

\frac{\partial}{\partial x} ((x - 1)^{2})

in v erse l a pl a ce \frac{3}{( s - 7 ) ^{4}}

\int arctan (8 t) d t