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^2sqrt(6x+4)

Lösung

\int x^{2} 6 x + 4 d x

Lösung

\frac{2 2}{2835} (135 x^{2} - 72 x + 32) (3 x + 2)^{\frac{3}{2}} + C

Schritte zur Lösung

\int x^{2} 6 x + 4 d x

Wende U-Substitution an

= \int \frac{u ( u - 4 ) ^{2}}{216} d u

Entferne die Konstante:

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

= \frac{1}{216} \cdot \int u (u - 4)^{2} d u

Multipliziere aus

u (u - 4)^{2} : u^{\frac{5}{2}} - 8 u^{\frac{3}{2}} + 16 u

= \frac{1}{216} \cdot \int u^{\frac{5}{2}} - 8 u^{\frac{3}{2}} + 16 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

= \frac{1}{216} (\int u^{\frac{5}{2}} d u - \int 8 u^{\frac{3}{2}} d u + \int 16 u d u)

\int u^{\frac{5}{2}} d u = \frac{2}{7} u^{\frac{7}{2}}

\int 8 u^{\frac{3}{2}} d u = \frac{16}{5} u^{\frac{5}{2}}

\int 16 u d u = \frac{32}{3} u^{\frac{3}{2}}

= \frac{1}{216} (\frac{2}{7} u^{\frac{7}{2}} - \frac{16}{5} u^{\frac{5}{2}} + \frac{32}{3} u^{\frac{3}{2}})

Setze in

u = 6 x + 4

ein

= \frac{1}{216} (\frac{2}{7} (6 x + 4)^{\frac{7}{2}} - \frac{16}{5} (6 x + 4)^{\frac{5}{2}} + \frac{32}{3} (6 x + 4)^{\frac{3}{2}})

Vereinfache

\frac{1}{216} (\frac{2}{7} (6 x + 4)^{\frac{7}{2}} - \frac{16}{5} (6 x + 4)^{\frac{5}{2}} + \frac{32}{3} (6 x + 4)^{\frac{3}{2}}) : \frac{2 2}{2835} (135 x^{2} - 72 x + 32) (3 x + 2)^{\frac{3}{2}}

= \frac{2 2}{2835} (135 x^{2} - 72 x + 32) (3 x + 2)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2 2}{2835} (135 x^{2} - 72 x + 32) (3 x + 2)^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

derivative-(3x)/2

d er i v a t i v e - \frac{3 x}{2}

derivative of 2x{z}(xcos(sin(x)))

\frac{d}{d x} (2 x z (x) cos (sin (x)))

(dx)/(dt)=3(x^2+1),x(pi/4)=1

\frac{d x}{d t} = 3 (x^{2} + 1), x (\frac{π}{4}) = 1

derivative f(x)=(2x-3)/(4-x)

d er i v a t i v e f (x) = \frac{2 x - 3}{4 - x}

(\partial)/(\partial x)(x/(1+x^2))

\frac{\partial}{\partial x} (\frac{x}{1 + x ^{2}})