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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{x ^{2}}{2} - \frac{4}{5} x^{\frac{5}{2}} + \frac{x ^{3}}{3} + C

Schritte zur Lösung

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

Multipliziere aus

(x - x)^{2} : x - 2 x^{\frac{3}{2}} + x^{2}

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

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

\int 2 x^{\frac{3}{2}} d x = \frac{4}{5} x^{\frac{5}{2}}

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

= \frac{x ^{2}}{2} - \frac{4}{5} x^{\frac{5}{2}} + \frac{x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} - \frac{4}{5} x^{\frac{5}{2}} + \frac{x ^{3}}{3} + C

Graph

Beliebte Beispiele

integral of (2x+3)sqrt(x^2+3x+5)

\int (2 x + 3) x^{2} + 3 x + 5 d x

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\int x^{5} - 3 x + \frac{2}{x} d x

integral of 1/(sqrt(x(x+2)))

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

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\int \frac{( arctan ( x ) ) ^{6}}{1 + x ^{2}} d x

integral of (5x^3)/(x^2+9)

\int \frac{5 x ^{3}}{x ^{2} + 9} d x