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Beliebt Rechnen >

integral of (x^5+2x^2-1)/(x^4)

Lösung

\int \frac{x ^{5} + 2 x ^{2} - 1}{x ^{4}} d x

Lösung

\frac{x ^{2}}{2} - \frac{2}{x} + \frac{1}{3 x ^{3}} + C

Schritte zur Lösung

\int \frac{x ^{5} + 2 x ^{2} - 1}{x ^{4}} d x

Multipliziere aus

\frac{x ^{5} + 2 x ^{2} - 1}{x ^{4}} : x + \frac{2}{x ^{2}} - \frac{1}{x ^{4}}

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

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

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

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

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

Vereinfache

= \frac{x ^{2}}{2} - \frac{2}{x} + \frac{1}{3 x ^{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} - \frac{2}{x} + \frac{1}{3 x ^{3}} + C

Graph

Beliebte Beispiele

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t an g e n t f (x) = (x - 2)^{\frac{1}{2}}, at x = 6

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d er i v a t i v e y = e^{c o s (3) x^{2}}

derivative of (6x^7/(5tan(x)))

\frac{d}{d x} (\frac{6 x ^{7}}{5 tan ( x )})

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\int \frac{1}{200 + 3 t} d t

integral of xe^{-x/4}

\int x e^{- \frac{x}{4}} d x