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Beliebt Rechnen >

integral of x^3(4x^2+5)

Lösung

\int x^{3} (4 x^{2} + 5) d x

Lösung

\frac{2 x ^{6}}{3} + \frac{5 x ^{4}}{4} + C

Schritte zur Lösung

\int x^{3} (4 x^{2} + 5) d x

Multipliziere aus

x^{3} (4 x^{2} + 5) : 4 x^{5} + 5 x^{3}

= \int 4 x^{5} + 5 x^{3} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 x^{5} d x + \int 5 x^{3} d x

\int 4 x^{5} d x = \frac{2 x ^{6}}{3}

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

= \frac{2 x ^{6}}{3} + \frac{5 x ^{4}}{4}

Füge eine Konstante zur Lösung hinzu

= \frac{2 x ^{6}}{3} + \frac{5 x ^{4}}{4} + C

Graph

Beliebte Beispiele

inverselaplace (6(s+34))/(s(s^2+10s+34))

in v erse l a pl a ce \frac{6 ( s + 34 )}{s ( s ^{2} + 10 s + 34 )}

normal f(x)=x^4+5e^x,(0,5)

n or ma l f (x) = x^{4} + 5 e^{x}, (0, 5)

derivative f(x)=ax

d er i v a t i v e f (x) = a x

integral from-infinity to 0 of x*e^x

\int_{- \infty}^{0} x \cdot e^{x} d x

(dx)/(dt)=x^2e^{-2t}

\frac{d x}{d t} = x^{2} e^{- 2 t}