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(x-1))

Lösung

\int x (x - 1) d x

Lösung

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

Schritte zur Lösung

\int x x - 1 d x

Wende U-Substitution an

= \int (u + 1) u d u

Multipliziere aus

(u + 1) u : u^{\frac{3}{2}} + u

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

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

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

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

Setze in

u = x - 1

ein

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative (10^x)/(ln(10))

d er i v a t i v e \frac{1 0 ^{x}}{ln ( 10 )}

integral of ax^n

\int a x^{n} d x

limit as x approaches-infinity of (x^3+x^2-3x+2)/(x^2-3x+1)

x \to - \infty lim (\frac{x ^{3} + x ^{2} - 3 x + 2}{x ^{2} - 3 x + 1})

derivative of-1/2 sin^2(x)

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

derivative 2x^2-x

d er i v a t i v e 2 x^{2} - x