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\sqrt[3]{2x+3}

Lösung

\int x 3 2 x + 3 d x

Lösung

\frac{1}{4} (\frac{3}{7} (2 x + 3)^{\frac{7}{3}} - \frac{9}{4} (2 x + 3)^{\frac{4}{3}}) + C

Schritte zur Lösung

\int x 3 2 x + 3 d x

Wende U-Substitution an

= \int \frac{3 u ( u - 3 )}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int 3 u (u - 3) d u

Multipliziere aus

3 u (u - 3) : u^{\frac{4}{3}} - 3 3 u

= \frac{1}{4} \cdot \int u^{\frac{4}{3}} - 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

= \frac{1}{4} (\int u^{\frac{4}{3}} d u - \int 3 3 u d u)

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

\int 3 3 u d u = \frac{9}{4} u^{\frac{4}{3}}

= \frac{1}{4} (\frac{3}{7} u^{\frac{7}{3}} - \frac{9}{4} u^{\frac{4}{3}})

Setze in

u = 2 x + 3

ein

= \frac{1}{4} (\frac{3}{7} (2 x + 3)^{\frac{7}{3}} - \frac{9}{4} (2 x + 3)^{\frac{4}{3}})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} (\frac{3}{7} (2 x + 3)^{\frac{7}{3}} - \frac{9}{4} (2 x + 3)^{\frac{4}{3}}) + C

Graph

Beliebte Beispiele

limit as x approaches+1 of 3x^3-4x^2+x+9

x \to + 1 lim (3 x^{3} - 4 x^{2} + x + 9)

derivative y=e^{x/2}

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

integral of 2xye^{x+y}

\int 2 x y e^{x + y} d x

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

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

y^'=-yt+0.1y^'t+4

y^{^{'}} = - y t + 0.1 y^{^{'}} t + 4