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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{4 x ^{3}}{3} - 12 x - \frac{9}{x} + C

Schritte zur Lösung

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

Multipliziere aus

(2 x - \frac{3}{x})^{2} : 4 x^{2} - 12 + \frac{9}{x ^{2}}

= \int 4 x^{2} - 12 + \frac{9}{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 4 x^{2} d x - \int 12 d x + \int \frac{9}{x ^{2}} d x

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

\int 12 d x = 12 x

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

= \frac{4 x ^{3}}{3} - 12 x - \frac{9}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{4 x ^{3}}{3} - 12 x - \frac{9}{x} + C

Graph

Beliebte Beispiele

steigung (-7,-9),(-2,-9)

s l o p e (- 7, - 9), (- 2, - 9)

integral of (x^{1.4}+7x^{2.5})

\int (x^{1.4} + 7 x^{2.5}) d x

derivative of (sqrt(x^2-2x)/(x^2))

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

t^3y^'+4t^2y=e^{-t},y(-1)=0

t^{3} y^{^{'}} + 4 t^{2} y = e^{- t}, y (- 1) = 0

integral of-3sin(x)

\int - 3 sin (x) d x