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Beliebt Rechnen >

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

Lösung

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

Lösung

9 x - 4 x^{\frac{3}{2}} + \frac{x ^{2}}{2} + C

Schritte zur Lösung

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

Multipliziere aus

(3 - x)^{2} : 9 - 6 x + x

= \int 9 - 6 x + 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

= \int 9 d x - \int 6 x d x + \int x d x

\int 9 d x = 9 x

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

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

= 9 x - 4 x^{\frac{3}{2}} + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= 9 x - 4 x^{\frac{3}{2}} + \frac{x ^{2}}{2} + C

Graph

Beliebte Beispiele

integral of x^2(x^2-49)^{3/2}

\int x^{2} (x^{2} - 49)^{\frac{3}{2}} d x

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\int \frac{13}{( x - 5 ) ( x + 8 )} d x

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\int (\frac{x ^{3} - 1}{x ^{2}}) d x

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\int e^{(x)^{2}} d x