de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (3x^2-6x^2+sqrt(x))/(x^3)

Lösung

\int \frac{3 x ^{2} - 6 x ^{2} + x}{x ^{3}} d x

Lösung

- 3 ln ∣ x ∣ - \frac{2}{3 x ^{\frac{3}{2}}} + C

Schritte zur Lösung

\int \frac{3 x ^{2} - 6 x ^{2} + x}{x ^{3}} d x

Vereinfache

= \int \frac{- 3 x ^{2} + x}{x ^{3}} d x

Multipliziere aus

\frac{- 3 x ^{2} + x}{x ^{3}} : - \frac{3}{x} + \frac{1}{x ^{\frac{5}{2}}}

= \int - \frac{3}{x} + \frac{1}{x ^{\frac{5}{2}}} d x

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{3}{x} d x + \int \frac{1}{x ^{\frac{5}{2}}} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int \frac{1}{x ^{\frac{5}{2}}} d x = - \frac{2}{3 x ^{\frac{3}{2}}}

= - 3 ln ∣ x ∣ - \frac{2}{3 x ^{\frac{3}{2}}}

Füge eine Konstante zur Lösung hinzu

= - 3 ln ∣ x ∣ - \frac{2}{3 x ^{\frac{3}{2}}} + C

Graph

Beliebte Beispiele

derivative g(w)=9\sqrt[3]{w}

d er i v a t i v e g (w) = 9 3 w

tangent y=sqrt(5x+20),\at x=1

t an g e n t y = 5 x + 20, at x = 1

derivative f(x)=16sqrt(x+3)

d er i v a t i v e f (x) = 16 x + 3

integral from-2 to 1 of x((4-x^2)-(x+2))

\int_{- 2}^{1} x ((4 - x^{2}) - (x + 2)) d x

dx=(e^{t^2}+2xt)dt

d x = (e^{t^{2}} + 2 x t) d t