de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (4x-16)/(sqrt(x)+2)

Lösung

\int \frac{4 x - 16}{x + 2} d x

Lösung

- 24 x - 32 x + \frac{8}{3} (x + 2)^{3} + 32 + C

Schritte zur Lösung

\int \frac{4 x - 16}{x + 2} d x

Multipliziere aus

\frac{4 x - 16}{x + 2} : \frac{4 x}{x + 2} - \frac{16}{x + 2}

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{4 x}{x + 2} d x - \int \frac{16}{x + 2} d x

\int \frac{4 x}{x + 2} d x = 8 (- 3 x + \frac{1}{3} (x + 2)^{3} - 8 ln x + 2 + 12)

\int \frac{16}{x + 2} d x = 32 (x + 2 - 2 ln x + 2)

= 8 (- 3 x + \frac{1}{3} (x + 2)^{3} - 8 ln x + 2 + 12) - 32 (x + 2 - 2 ln x + 2)

Vereinfache

8 (- 3 x + \frac{1}{3} (x + 2)^{3} - 8 ln x + 2 + 12) - 32 (x + 2 - 2 ln x + 2) : - 24 x - 32 x + \frac{8}{3} (x + 2)^{3} + 32

= - 24 x - 32 x + \frac{8}{3} (x + 2)^{3} + 32

Füge eine Konstante zur Lösung hinzu

= - 24 x - 32 x + \frac{8}{3} (x + 2)^{3} + 32 + C

Graph

Beliebte Beispiele

integral of sec^2(3x)tan^4(3x)

\int sec^{2} (3 x) tan^{4} (3 x) d x

integral of 1/((x+3)^{3/2)}

\int \frac{1}{( x + 3 ) ^{\frac{3}{2}}} d x

integral of sin(7x+3pi)

\int sin (7 x + 3 π) d x

integral of (sin(x))^5(cos(x))^4

\int (sin (x))^{5} (cos (x))^{4} d x

integral of 2xsqrt(4-x)

\int 2 x 4 - x d x