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)+4)

Lösung

\int \frac{x}{x + 4} d x

Lösung

x - 8 x + 32 ln x + 4 - 48 + C

Schritte zur Lösung

\int \frac{x}{x + 4} d x

Wende U-Substitution an

= \int \frac{2 ( u ^{2} - 8 u + 16 )}{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} - 8 u + 16}{u} d u

Multipliziere aus

\frac{u ^{2} - 8 u + 16}{u} : u - 8 + \frac{16}{u}

= 2 \cdot \int u - 8 + \frac{16}{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 8 d u + \int \frac{16}{u} d u)

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

\int 8 d u = 8 u

\int \frac{16}{u} d u = 16 ln ∣ u ∣

= 2 (\frac{u ^{2}}{2} - 8 u + 16 ln ∣ u ∣)

Setze in

u = x + 4

ein

= 2 (\frac{( x + 4 ) ^{2}}{2} - 8 (x + 4) + 16 ln x + 4)

Vereinfache

2 (\frac{( x + 4 ) ^{2}}{2} - 8 (x + 4) + 16 ln x + 4) : x - 8 x + 32 ln x + 4 - 48

= x - 8 x + 32 ln x + 4 - 48

Füge eine Konstante zur Lösung hinzu

= x - 8 x + 32 ln x + 4 - 48 + C

Graph

Beliebte Beispiele

integral of xtan(8)x^2

\int x tan (8) x^{2} d x

integral of (pi+3)/(e^{3x)}

\int \frac{π + 3}{e ^{3 x}} d x

integral of 1/(sqrt(x-17))

\int \frac{1}{x - 17} d x

integral of (sqrt(x)+sqrt(a))^2x

\int (x + a)^{2} x d x

integral of sqrt(x^2-4x-5)

\int x^{2} - 4 x - 5 d x