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Beliebt Rechnen >

integral of (x^2-4)^2(2x)

Lösung

\int (x^{2} - 4)^{2} (2 x) d x

Lösung

2 (\frac{x ^{6}}{6} - 2 x^{4} + 8 x^{2}) + C

Schritte zur Lösung

\int (x^{2} - 4)^{2} \cdot 2 x d x

Entferne die Konstante:

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

= 2 \cdot \int (x^{2} - 4)^{2} x d x

Multipliziere aus

(x^{2} - 4)^{2} x : x^{5} - 8 x^{3} + 16 x

= 2 \cdot \int x^{5} - 8 x^{3} + 16 x 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

= 2 (\int x^{5} d x - \int 8 x^{3} d x + \int 16 x d x)

\int x^{5} d x = \frac{x ^{6}}{6}

\int 8 x^{3} d x = 2 x^{4}

\int 16 x d x = 8 x^{2}

= 2 (\frac{x ^{6}}{6} - 2 x^{4} + 8 x^{2})

Füge eine Konstante zur Lösung hinzu

= 2 (\frac{x ^{6}}{6} - 2 x^{4} + 8 x^{2}) + C

Graph

Beliebte Beispiele

integral of 13sin^3(xco)s^2x

\int 13 sin^{3} (x co) s^{2} x d x

integral of (arctan(sqrt(x)))/(sqrt(x))

\int \frac{arctan ( x )}{x} d x

f(x)=tan^4(x^3)

f (x) = tan^{4} (x^{3})

limit as x approaches 0 of 5/(x^2)

x \to 0 lim (\frac{5}{x ^{2}})

derivative ln(3x^3+6x^2+2x+6)

d er i v a t i v e ln (3 x^{3} + 6 x^{2} + 2 x + 6)