integral of x/(x-9)

Lösung

\int \frac{x}{x - 9} d x

x - 9 + 9 ln ∣ x - 9 ∣ + C

Schritte zur Lösung

\int \frac{x}{x - 9} d x

Wende U-Substitution an

= \int \frac{u + 9}{u} d u

Multipliziere aus

\frac{u + 9}{u} : 1 + \frac{9}{u}

= \int 1 + \frac{9}{u} d u

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 u + \int \frac{9}{u} d u

\int 1 d u = u

\int \frac{9}{u} d u = 9 ln ∣ u ∣

= u + 9 ln ∣ u ∣

Setze in

u = x - 9

ein

= x - 9 + 9 ln ∣ x - 9 ∣

Füge eine Konstante zur Lösung hinzu

= x - 9 + 9 ln ∣ x - 9 ∣ + C

d er i v a t i v e sin^{5} (x^{3})

x \to 5 lim (∣ x - 5 ∣)

\int - \frac{2}{100 - 9 t ^{2}} d t

\frac{\partial}{\partial x} (x^{2} + y^{2} - 5)

t an g e n t f (x) = x^{3} - x, at x = 1