de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of x^2*\sqrt[3]{1-x}

Lösung

\int x^{2} \cdot 3 1 - x d x

Lösung

- \frac{3}{10} (1 - x)^{\frac{10}{3}} + \frac{6}{7} (1 - x)^{\frac{7}{3}} - \frac{3}{4} (1 - x)^{\frac{4}{3}} + C

Schritte zur Lösung

\int x^{2} 3 1 - x d x

Wende U-Substitution an

= \int - (- u + 1)^{2} 3 u d u

Entferne die Konstante:

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

= - \int (- u + 1)^{2} 3 u d u

Multipliziere aus

(- u + 1)^{2} 3 u : u^{\frac{7}{3}} - 2 u^{\frac{4}{3}} + 3 u

= - \int u^{\frac{7}{3}} - 2 u^{\frac{4}{3}} + 3 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

= - (\int u^{\frac{7}{3}} d u - \int 2 u^{\frac{4}{3}} d u + \int 3 u d u)

\int u^{\frac{7}{3}} d u = \frac{3}{10} u^{\frac{10}{3}}

\int 2 u^{\frac{4}{3}} d u = \frac{6}{7} u^{\frac{7}{3}}

\int 3 u d u = \frac{3}{4} u^{\frac{4}{3}}

= - (\frac{3}{10} u^{\frac{10}{3}} - \frac{6}{7} u^{\frac{7}{3}} + \frac{3}{4} u^{\frac{4}{3}})

Setze in

u = 1 - x

ein

= - (\frac{3}{10} (1 - x)^{\frac{10}{3}} - \frac{6}{7} (1 - x)^{\frac{7}{3}} + \frac{3}{4} (1 - x)^{\frac{4}{3}})

Vereinfache

= - \frac{3}{10} (1 - x)^{\frac{10}{3}} + \frac{6}{7} (1 - x)^{\frac{7}{3}} - \frac{3}{4} (1 - x)^{\frac{4}{3}}

Füge eine Konstante zur Lösung hinzu

= - \frac{3}{10} (1 - x)^{\frac{10}{3}} + \frac{6}{7} (1 - x)^{\frac{7}{3}} - \frac{3}{4} (1 - x)^{\frac{4}{3}} + C

Graph

Beliebte Beispiele

integral of sqrt(3)

\int 3 d x

tangent y=arctan(-x),\at x=4

t an g e n t y = arctan (- x), at x = 4

derivative y=x^4e^{2x}

d er i v a t i v e y = x^{4} e^{2 x}

limit as x approaches 0+of 4/x-4/(|x|)

x \to 0 + lim (\frac{4}{x} - \frac{4}{∣ x ∣})

steigung (790,77880),(970,94440)

s l o p e (790, 77880), (970, 94440)