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-8)}

Lösung

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

Lösung

\frac{3}{5} (x - 8)^{\frac{5}{3}} + 12 (x - 8)^{\frac{2}{3}} + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{u + 8}{3 u} d u

Multipliziere aus

\frac{u + 8}{3 u} : u^{\frac{2}{3}} + \frac{8}{3 u}

= \int u^{\frac{2}{3}} + \frac{8}{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{8}{3 u} d u

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

\int \frac{8}{3 u} d u = 12 u^{\frac{2}{3}}

= \frac{3}{5} u^{\frac{5}{3}} + 12 u^{\frac{2}{3}}

Setze in

u = x - 8

ein

= \frac{3}{5} (x - 8)^{\frac{5}{3}} + 12 (x - 8)^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{5} (x - 8)^{\frac{5}{3}} + 12 (x - 8)^{\frac{2}{3}} + C

Graph

Beliebte Beispiele

derivative of e^{0.1x^2}

\frac{d}{d x} (e^{0.1 x^{2}})

derivative of e^x-x^2+3x-2

\frac{d}{d x} (e^{x} - x^{2} + 3 x - 2)

integral from-2 to 3 of (17)/(x^4)

\int_{- 2}^{3} \frac{17}{x ^{4}} d x

y^{^{''}} = 2 y^{^{'}} + 8 y

integral of 4/3 e^{4x}

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