de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of ((u^3+2u^2-u)/(3u))

Lösung

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

Lösung

\frac{1}{3} (\frac{u ^{3}}{3} + u^{2} - u) + C

Schritte zur Lösung

\int \frac{u ^{3} + 2 u ^{2} - u}{3 u} d u

Entferne die Konstante:

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

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

Multipliziere aus

\frac{u ^{3} + 2 u ^{2} - u}{u} : \frac{u ^{3}}{u} + \frac{2 u ^{2}}{u} - \frac{u}{u}

Wende die Summenregel an:

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

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} (\frac{u ^{3}}{3} + u^{2} - u) + C

Graph

Beliebte Beispiele

integral of (3x^2)/((196+x^2)^2)

\int \frac{3 x ^{2}}{( 196 + x ^{2} ) ^{2}} d x

integral of ax^4+bx^3+3c

\int a x^{4} + b x^{3} + 3 c d x

integral of x/(x^4-2x^3+2x^2-2x+1)

\int \frac{x}{x ^{4} - 2 x ^{3} + 2 x ^{2} - 2 x + 1} d x

integral of (5^y+(6x)/(y+4))

\int (5^{y} + \frac{6 x}{y + 4}) d x

integral of 10x^{-1}

\int 10 x^{- 1} d x