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Beliebt Rechnen >

integral of x/(x-8)

Lösung

\int \frac{x}{x - 8} d x

Lösung

x - 8 + 8 ln ∣ x - 8 ∣ + C

Schritte zur Lösung

\int \frac{x}{x - 8} d x

Wende U-Substitution an

= \int \frac{u + 8}{u} d u

Multipliziere aus

\frac{u + 8}{u} : 1 + \frac{8}{u}

= \int 1 + \frac{8}{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{8}{u} d u

\int 1 d u = u

\int \frac{8}{u} d u = 8 ln ∣ u ∣

= u + 8 ln ∣ u ∣

Setze in

u = x - 8

ein

= x - 8 + 8 ln ∣ x - 8 ∣

Füge eine Konstante zur Lösung hinzu

= x - 8 + 8 ln ∣ x - 8 ∣ + C

Graph

Beliebte Beispiele

y^{''}-2y^'+9y=0

y^{^{''}} - 2 y^{^{'}} + 9 y = 0

(\partial)/(\partial x)(e^{xy}+y/x)

\frac{\partial}{\partial x} (e^{x y} + \frac{y}{x})

derivative g(x)= 9/(x^3)

d er i v a t i v e g (x) = \frac{9}{x ^{3}}

(\partial)/(\partial x)(x^2-3xy^2)

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integral of (25)/(1+25x^2)

\int \frac{25}{1 + 25 x ^{2}} d x