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Beliebt Rechnen >

integral of (x^5-3x)/(x^4)

Lösung

\int \frac{x ^{5} - 3 x}{x ^{4}} d x

Lösung

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

Schritte zur Lösung

\int \frac{x ^{5} - 3 x}{x ^{4}} d x

Multipliziere aus

\frac{x ^{5} - 3 x}{x ^{4}} : x - \frac{3}{x ^{3}}

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

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

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

= \frac{x ^{2}}{2} - (- \frac{3}{2 x ^{2}})

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

fläche y=x^2+1,x=0,x=6

a re a y = x^{2} + 1, x = 0, x = 6

integral of-4sin(2x)+3

\int - 4 sin (2 x) + 3 d x

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\int \frac{1}{2 x + 3} d x

derivative of (1/2 x^2-3^2)

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

(d^2}{dx^2}(\frac{ln(x))/x)

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