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Beliebt Rechnen >

integral of ((x^4-5x^2+3x-4))/x

Lösung

\int \frac{( x ^{4} - 5 x ^{2} + 3 x - 4 )}{x} d x

Lösung

\frac{x ^{4}}{4} - \frac{5 x ^{2}}{2} + 3 x - 4 ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{x ^{4} - 5 x ^{2} + 3 x - 4}{x} d x

Multipliziere aus

\frac{x ^{4} - 5 x ^{2} + 3 x - 4}{x} : x^{3} - 5 x + 3 - \frac{4}{x}

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

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

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

\int 3 d x = 3 x

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= \frac{x ^{4}}{4} - \frac{5 x ^{2}}{2} + 3 x - 4 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} - \frac{5 x ^{2}}{2} + 3 x - 4 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral from 1 to e of ((x^2-1)/x)

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

derivative of ln((x+y/(x-y)))

\frac{d}{d x} (ln (\frac{x + y}{x - y}))

derivative of ln(2x^4e^{3x}(x^2+x+1^5))

\frac{d}{d x} (ln (2 x^{4} e^{3 x} (x^{2} + x + 1)^{5}))

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

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

integral from-2 to 5 of-2

\int_{- 2}^{5} - 2 d x