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[3]{x}-1/x)^2

Lösung

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

Lösung

- \frac{1}{x} - 6 3 x + \frac{3}{5} x^{\frac{5}{3}} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

\int \frac{2}{x ^{\frac{2}{3}}} d x = 6 x^{\frac{1}{3}}

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

= - \frac{1}{x} - 6 x^{\frac{1}{3}} + \frac{3}{5} x^{\frac{5}{3}}

Wende Radikal Regel an:

a^{\frac{1}{n}} = n a

= - \frac{1}{x} - 6 3 x + \frac{3}{5} x^{\frac{5}{3}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{x} - 6 3 x + \frac{3}{5} x^{\frac{5}{3}} + C

Graph

Beliebte Beispiele

tangent f(x)= 1/(sqrt(x+1)),(0,1)

t an g e n t f (x) = \frac{1}{x + 1}, (0, 1)

fläche y=6e^x,y=6e^{-x},x=1

a re a y = 6 e^{x}, y = 6 e^{- x}, x = 1

integral of 1/(y^2-9)

\int \frac{1}{y ^{2} - 9} d y

derivative y(θ)=pi^4cos(θ)

d er i v a t i v e y (θ) = π^{4} cos (θ)

d/(dt)(sqrt(9+t))

\frac{d}{d t} (9 + t)