de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of ((6x^512x^4+9x^3)/(3x^2))

Lösung

\int (\frac{6 x ^{5} 12 x ^{4} + 9 x ^{3}}{3 x ^{2}}) d x

Lösung

\frac{3}{2} x^{2} (2 x^{6} + 1) + C

Schritte zur Lösung

\int \frac{6 x ^{5} \cdot 12 x ^{4} + 9 x ^{3}}{3 x ^{2}} d x

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int \frac{6 x ^{5} \cdot 12 x ^{4} + 9 x ^{3}}{x ^{2}} d x

Multipliziere aus

\frac{6 x ^{5} 12 x ^{4} + 9 x ^{3}}{x ^{2}} : \frac{6 x ^{5} \cdot 12 x ^{4}}{x ^{2}} + \frac{9 x ^{3}}{x ^{2}}

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}{3} (\int \frac{6 x ^{5} \cdot 12 x ^{4}}{x ^{2}} d x + \int \frac{9 x ^{3}}{x ^{2}} d x)

\int \frac{6 x ^{5} \cdot 12 x ^{4}}{x ^{2}} d x = 9 x^{8}

\int \frac{9 x ^{3}}{x ^{2}} d x = \frac{9 x ^{2}}{2}

= \frac{1}{3} (9 x^{8} + \frac{9 x ^{2}}{2})

Vereinfache

\frac{1}{3} (9 x^{8} + \frac{9 x ^{2}}{2}) : \frac{3}{2} x^{2} (2 x^{6} + 1)

= \frac{3}{2} x^{2} (2 x^{6} + 1)

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} x^{2} (2 x^{6} + 1) + C

Graph

Beliebte Beispiele

inverselaplace 1/((s^2+1)(s^2+4s+8))

in v erse l a pl a ce \frac{1}{( s ^{2} + 1 ) ( s ^{2} + 4 s + 8 )}

derivative f(x)=sqrt(x^2+5)

d er i v a t i v e f (x) = x^{2} + 5

y y^{^{'}} - 16 e^{x} = 0

d/(dy)(e^{-y^2})

\frac{d}{d y} (e^{- y^{2}})

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

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