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Beliebt Rechnen >

integral of (x^4-1)x^2

Lösung

\int (x^{4} - 1) x^{2} d x

Lösung

\frac{x ^{7}}{7} - \frac{x ^{3}}{3} + C

Schritte zur Lösung

\int (x^{4} - 1) x^{2} d x

Multipliziere aus

(x^{4} - 1) x^{2} : x^{6} - x^{2}

= \int x^{6} - x^{2} 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 x^{6} d x - \int x^{2} d x

\int x^{6} d x = \frac{x ^{7}}{7}

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

= \frac{x ^{7}}{7} - \frac{x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{7}}{7} - \frac{x ^{3}}{3} + C

Graph

Beliebte Beispiele

(dy)/(dx)=y(2-3y)

\frac{d y}{d x} = y (2 - 3 y)

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integral of 2sin(x)-3cos(x)

\int 2 sin (x) - 3 cos (x) d x

tangent f(x)=(x^2)/(x+2),\at x=3

t an g e n t f (x) = \frac{x ^{2}}{x + 2}, at x = 3

integral of (6x^6-2)^2(36x)

\int (6 x^{6} - 2)^{2} (36 x) d x