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Beliebt Rechnen >

integral of (2x)/(x-4)

Lösung

\int \frac{2 x}{x - 4} d x

Lösung

2 (x - 4 + 4 ln ∣ x - 4 ∣) + C

Schritte zur Lösung

\int \frac{2 x}{x - 4} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{x}{x - 4} d x

Wende U-Substitution an

= 2 \cdot \int \frac{u + 4}{u} d u

Multipliziere aus

\frac{u + 4}{u} : 1 + \frac{4}{u}

= 2 \cdot \int 1 + \frac{4}{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

= 2 (\int 1 d u + \int \frac{4}{u} d u)

\int 1 d u = u

\int \frac{4}{u} d u = 4 ln ∣ u ∣

= 2 (u + 4 ln ∣ u ∣)

Setze in

u = x - 4

ein

= 2 (x - 4 + 4 ln ∣ x - 4 ∣)

Füge eine Konstante zur Lösung hinzu

= 2 (x - 4 + 4 ln ∣ x - 4 ∣) + C

Graph

Beliebte Beispiele

(x^2+5)dx+(y-3)(x-2)dy=0

(x^{2} + 5) d x + (y - 3) (x - 2) d y = 0

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\int 12 tan^{3} (x) d x

integral from 0 to 1 of (42)/(4y-1)

\int_{0}^{1} \frac{42}{4 y - 1} d y

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y^{^{''}} = 6 x + 2, y (1) = - 1, y^{^{'}} (1) = 7

(\partial)/(\partial z)(arctan(x^2yz^2))

\frac{\partial}{\partial z} (arctan (x^{2} y z^{2}))