de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (6-6x)/(1-sqrt(x))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende U-Substitution an

= \int 12 u (u + 1) d u

Entferne die Konstante:

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

= 12 \cdot \int u (u + 1) d u

Multipliziere aus

u (u + 1) : u^{2} + u

= 12 \cdot \int u^{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

= 12 (\int u^{2} d u + \int u d u)

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

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

= 12 (\frac{u ^{3}}{3} + \frac{u ^{2}}{2})

Setze in

u = x

ein

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

Vereinfache

12 (\frac{( x ) ^{3}}{3} + \frac{( x ) ^{2}}{2}) : 12 (\frac{1}{3} x^{\frac{3}{2}} + \frac{x}{2})

= 12 (\frac{1}{3} x^{\frac{3}{2}} + \frac{x}{2})

Füge eine Konstante zur Lösung hinzu

= 12 (\frac{1}{3} x^{\frac{3}{2}} + \frac{x}{2}) + C

Graph

Beliebte Beispiele

derivative of 1/8 xsqrt(64-x^2)

\frac{d}{d x} (\frac{1}{8} x 64 - x^{2})

slopeintercept (5,-4),(4,7)

s l o p e in t erce pt (5, - 4), (4, 7)

integral of 7/(xsqrt(36-49ln^2(x)))

\int \frac{7}{x 36 - 49 ln ^{2} ( x )} d x

derivative of xsin(x+cos(x))

\frac{d}{d x} (x sin (x) + cos (x))

integral of sqrt(13+12x-x^2)

\int 13 + 12 x - x^{2} d x