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Beliebt Rechnen >

integral of (1-2x^2-4/(x^{-3)})x^{-3}

Lösung

\int (1 - 2 x^{2} - \frac{4}{x ^{- 3}}) x^{- 3} d x

Lösung

- \frac{1}{2 x ^{2}} - 2 ln ∣ x ∣ - 4 x + C

Schritte zur Lösung

\int (1 - 2 x^{2} - \frac{4}{x ^{- 3}}) x^{- 3} d x

Vereinfache

(1 - 2 x^{2} - \frac{4}{x ^{- 3}}) x^{- 3} : \frac{1 - 2 x ^{2} - 4 x ^{3}}{x ^{3}}

= \int \frac{1 - 2 x ^{2} - 4 x ^{3}}{x ^{3}} d x

Multipliziere aus

\frac{1 - 2 x ^{2} - 4 x ^{3}}{x ^{3}} : \frac{1}{x ^{3}} - \frac{2}{x} - 4

= \int \frac{1}{x ^{3}} - \frac{2}{x} - 4 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{1}{x ^{3}} d x - \int \frac{2}{x} d x - \int 4 d x

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 4 d x = 4 x

= - \frac{1}{2 x ^{2}} - 2 ln ∣ x ∣ - 4 x

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2 x ^{2}} - 2 ln ∣ x ∣ - 4 x + C

Graph

Beliebte Beispiele

integral of (7x^2-12x)e^{2x}

\int (7 x^{2} - 12 x) e^{2 x} d x

limit as x approaches infinity of x/(\sqrt[3]{x^3+7)}

x \to \infty lim (\frac{x}{3 x ^{3} + 7})

limit as x approaches-2-of-3x^2+2

x \to - 2 - lim (- 3 x^{2} + 2)

y^'= 1/2+1/4 sin(t)-y/(50)

y^{^{'}} = \frac{1}{2} + \frac{1}{4} sin (t) - \frac{y}{50}

integral of a/(b^{3θ)}

\int \frac{a}{b ^{3 θ}} d θ