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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{4}{x} - \frac{2}{9} x^{\frac{9}{2}} + \frac{4}{5} x^{\frac{5}{2}} + C

Schritte zur Lösung

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

Multipliziere aus

x (\frac{2}{x ^{2}} - x^{3} + 2 x) : \frac{2}{x ^{\frac{3}{2}}} - x^{\frac{7}{2}} + 2 x^{\frac{3}{2}}

= \int \frac{2}{x ^{\frac{3}{2}}} - x^{\frac{7}{2}} + 2 x^{\frac{3}{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 \frac{2}{x ^{\frac{3}{2}}} d x - \int x^{\frac{7}{2}} d x + \int 2 x^{\frac{3}{2}} d x

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

\int x^{\frac{7}{2}} d x = \frac{2}{9} x^{\frac{9}{2}}

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

= - \frac{4}{x} - \frac{2}{9} x^{\frac{9}{2}} + \frac{4}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= - \frac{4}{x} - \frac{2}{9} x^{\frac{9}{2}} + \frac{4}{5} x^{\frac{5}{2}} + C

Graph

Beliebte Beispiele

integral of (x^2+9x+2)/((x-1)(x+1)(x+2))

\int \frac{x ^{2} + 9 x + 2}{( x - 1 ) ( x + 1 ) ( x + 2 )} d x

integral of sin(0.01t)+t^3

\int sin (0.01 t) + t^{3} d t

integral of x(7-x^2)

\int x (7 - x^{2}) d x

integral of log_{3}(6x^2)x

\int lo g_{3} (6 x^{2}) x d x

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

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