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Beliebt Rechnen >

integral of (x^2-sqrt(x)+3)

Lösung

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

Lösung

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

Schritte zur Lösung

\int x^{2} - 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 x^{2} d x - \int x d x + \int 3 d x

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

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

\int 3 d x = 3 x

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (2x)/(x^2+y^4)

\int \frac{2 x}{x ^{2} + y ^{4}} d x

tangent f(x)= 1/(sqrt(2x))x^9

t an g e n t f (x) = \frac{1}{2 x} x^{9}

slopeintercept (-1,7),(3,-1)

s l o p e in t erce pt (- 1, 7), (3, - 1)

limit as x approaches 0 of (arccos(1-x))/(sqrt(x))

x \to 0 lim (\frac{arccos ( 1 - x )}{x})

tangent x^2+y^2=169,(-12,5)

t an g e n t x^{2} + y^{2} = 169, (- 12, 5)