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+1)}

Lösung

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

Lösung

\frac{1}{4} (\frac{3}{5} (2 x + 1)^{\frac{5}{3}} - \frac{3}{2} (2 x + 1)^{\frac{2}{3}}) + C

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Multipliziere aus

\frac{u - 1}{3 u} : u^{\frac{2}{3}} - \frac{1}{3 u}

= \frac{1}{4} \cdot \int u^{\frac{2}{3}} - \frac{1}{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{2}{3}} d u - \int \frac{1}{3 u} d u)

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

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

= \frac{1}{4} (\frac{3}{5} u^{\frac{5}{3}} - \frac{3}{2} u^{\frac{2}{3}})

Setze in

u = 2 x + 1

ein

= \frac{1}{4} (\frac{3}{5} (2 x + 1)^{\frac{5}{3}} - \frac{3}{2} (2 x + 1)^{\frac{2}{3}})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} (\frac{3}{5} (2 x + 1)^{\frac{5}{3}} - \frac{3}{2} (2 x + 1)^{\frac{2}{3}}) + C

Graph

Beliebte Beispiele

integral of sqrt(36x^2+36x^4)

\int 36 x^{2} + 36 x^{4} d x

integral of (2-cot(x))(1-csc(x))

\int (2 - cot (x)) (1 - csc (x)) d x

integral of e^{-2x-3y}

\int e^{- 2 x - 3 y} d y

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

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

integral of ((ln(t))^5)/t

\int \frac{( ln ( t ) ) ^{5}}{t} d t