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^3-3x+1)/(y+sqrt(y))

Lösung

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

Lösung

\frac{1 - y}{y ( 1 - y )} (x + \frac{x ^{4}}{4} - \frac{3 x ^{2}}{2}) + C

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Vereinfache

\frac{1}{y + y} : \frac{1 - y}{y ( 1 - y )}

= \frac{1 - y}{y ( 1 - y )} \cdot \int 1 + x^{3} - 3 x 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

= \frac{1 - y}{y ( 1 - y )} (\int 1 d x + \int x^{3} d x - \int 3 x d x)

\int 1 d x = x

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

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

= \frac{1 - y}{y ( 1 - y )} (x + \frac{x ^{4}}{4} - \frac{3 x ^{2}}{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1 - y}{y ( 1 - y )} (x + \frac{x ^{4}}{4} - \frac{3 x ^{2}}{2}) + C

Graph

Beliebte Beispiele

integral of (4e^{-0.8x})

\int (4 e^{- 0.8 x}) d x

(dx)/(dt)=e^{-kt}

\frac{d x}{d t} = e^{- k t}

fläche x^2,x^3

a re a x^{2}, x^{3}

(\partial)/(\partial y)((x^2+y^2)^{3/2})

\frac{\partial}{\partial y} ((x^{2} + y^{2})^{\frac{3}{2}})

(\partial)/(\partial x)(arctan(y/(x+a)))

\frac{\partial}{\partial x} (arctan (\frac{y}{x + a}))