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Beliebt Rechnen >

integral of (x^2+x+1)

Lösung

\int (x^{2} + x + 1) d x

Lösung

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x + C

Schritte zur Lösung

\int x^{2} + x + 1 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^{2} d x + \int x d x + \int 1 d x

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

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

\int 1 d x = x

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x + C

Graph

Beliebte Beispiele

integral of cos(θ)sin^2(θ)

\int cos (θ) sin^{2} (θ) d θ

(\partial)/(\partial y)(x^2cos(e^{xy}))

\frac{\partial}{\partial y} (x^{2} cos (e^{x y}))

y^{''}+6y^'+9y=-xe^{4x}

y^{^{''}} + 6 y^{^{'}} + 9 y = - x e^{4 x}

integral of (8x)/(x^2+x+1)

\int \frac{8 x}{x ^{2} + x + 1} d x

limit as x approaches-2 of x^2-1

x \to - 2 lim (x^{2} - 1)