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]{x+3)}

Lösung

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

Lösung

\frac{3}{5} (x + 3)^{\frac{5}{3}} - \frac{9}{2} (x + 3)^{\frac{2}{3}} + C

Schritte zur Lösung

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

Wende U-Substitution an

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

Multipliziere aus

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

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

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

\int \frac{3}{3 u} d u = \frac{9}{2} u^{\frac{2}{3}}

= \frac{3}{5} u^{\frac{5}{3}} - \frac{9}{2} u^{\frac{2}{3}}

Setze in

u = x + 3

ein

= \frac{3}{5} (x + 3)^{\frac{5}{3}} - \frac{9}{2} (x + 3)^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{5} (x + 3)^{\frac{5}{3}} - \frac{9}{2} (x + 3)^{\frac{2}{3}} + C

Graph

Beliebte Beispiele

integral of 8x^{-3/2}

\int 8 x^{- \frac{3}{2}} d x

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

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

integral of x^2e^{x^3-5}

\int x^{2} e^{x^{3} - 5} d x

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

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

integral of (1-sin^3(x))

\int (1 - sin^{3} (x)) d x