de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (5x-6)/(\sqrt[3]{x-1)}

Lösung

\int \frac{5 x - 6}{3 x - 1} d x

Lösung

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

Schritte zur Lösung

\int \frac{5 x - 6}{3 x - 1} d x

Wende U-Substitution an

= \int \frac{5 u - 1}{3 u} d u

Multipliziere aus

\frac{5 u - 1}{3 u} : 5 u^{\frac{2}{3}} - \frac{1}{3 u}

= \int 5 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

= \int 5 u^{\frac{2}{3}} d u - \int \frac{1}{3 u} d u

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

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

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

Setze in

u = x - 1

ein

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (3x)/(3x+1)

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

integral of (2x+5)/(5x+9)

\int \frac{2 x + 5}{5 x + 9} d x

integral of ((ln(x)+1))/x

\int \frac{( ln ( x ) + 1 )}{x} d x

integral of e^{x^3}*3x^2

\int e^{x^{3}} \cdot 3 x^{2} d x

integral of (3x^2-2x+4)/(x+2)

\int \frac{3 x ^{2} - 2 x + 4}{x + 2} d x