de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (sqrt(x))/(sqrt(x)-5)

Lösung

\int \frac{x}{x - 5} d x

Lösung

x + 10 x + 50 ln x - 5 - 75 + C

Schritte zur Lösung

\int \frac{x}{x - 5} d x

Wende U-Substitution an

= \int \frac{2 ( u ^{2} + 10 u + 25 )}{u} d u

Entferne die Konstante:

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

= 2 \cdot \int \frac{u ^{2} + 10 u + 25}{u} d u

Multipliziere aus

\frac{u ^{2} + 10 u + 25}{u} : u + 10 + \frac{25}{u}

= 2 \cdot \int u + 10 + \frac{25}{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 u d u + \int 10 d u + \int \frac{25}{u} d u)

\int u d u = \frac{u ^{2}}{2}

\int 10 d u = 10 u

\int \frac{25}{u} d u = 25 ln ∣ u ∣

= 2 (\frac{u ^{2}}{2} + 10 u + 25 ln ∣ u ∣)

Setze in

u = x - 5

ein

= 2 (\frac{( x - 5 ) ^{2}}{2} + 10 (x - 5) + 25 ln x - 5)

Vereinfache

2 (\frac{( x - 5 ) ^{2}}{2} + 10 (x - 5) + 25 ln x - 5) : x + 10 x + 50 ln x - 5 - 75

= x + 10 x + 50 ln x - 5 - 75

Füge eine Konstante zur Lösung hinzu

= x + 10 x + 50 ln x - 5 - 75 + C

Graph

Beliebte Beispiele

derivative f(x)= 1/(2sqrt(x))

d er i v a t i v e f (x) = \frac{1}{2 x}

limit as x approaches 2 of (x+1)(3x^2-9)

x \to 2 lim ((x + 1) (3 x^{2} - 9))

fläche 2x^2+5,[-2,3]

a re a 2 x^{2} + 5, [- 2, 3]

limit as x approaches 1 of (|1-x|)/(1-x)

x \to 1 lim (\frac{∣ 1 - x ∣}{1 - x})

derivative of ln(x^8y)

\frac{d}{d x} (ln (x^{8} y))