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Beliebt Rechnen >

integral of ((x^3+1)/(x^5))

Lösung

\int (\frac{x ^{3} + 1}{x ^{5}}) d x

Lösung

- \frac{1}{x} - \frac{1}{4 x ^{4}} + C

Schritte zur Lösung

\int \frac{x ^{3} + 1}{x ^{5}} d x

Multipliziere aus

\frac{x ^{3} + 1}{x ^{5}} : \frac{1}{x ^{2}} + \frac{1}{x ^{5}}

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

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

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

= - \frac{1}{x} - \frac{1}{4 x ^{4}}

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of ln(w)

\int ln (w) d w

integral of (8-2x)^2

\int (8 - 2 x)^{2} d x

integral of (x^4-x^2y^4)

\int (x^{4} - x^{2} y^{4}) d x

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\int \frac{8 x ^{2}}{x ^{3} + 2} d x

integral of (x^2+3x+2)/(x^4-x^2)

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