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Beliebt Rechnen >

integral of (x^4+2x^3-7x^2+5x-2)/x

Lösung

\int \frac{x ^{4} + 2 x ^{3} - 7 x ^{2} + 5 x - 2}{x} d x

Lösung

\frac{x ^{4}}{4} + \frac{2 x ^{3}}{3} - \frac{7 x ^{2}}{2} + 5 x - 2 ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{x ^{4} + 2 x ^{3} - 7 x ^{2} + 5 x - 2}{x} d x

Multipliziere aus

\frac{x ^{4} + 2 x ^{3} - 7 x ^{2} + 5 x - 2}{x} : x^{3} + 2 x^{2} - 7 x + 5 - \frac{2}{x}

= \int x^{3} + 2 x^{2} - 7 x + 5 - \frac{2}{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 2 x^{2} d x - \int 7 x d x + \int 5 d x - \int \frac{2}{x} d x

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

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

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 5 d x = 5 x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{x ^{4}}{4} + \frac{2 x ^{3}}{3} - \frac{7 x ^{2}}{2} + 5 x - 2 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} + \frac{2 x ^{3}}{3} - \frac{7 x ^{2}}{2} + 5 x - 2 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of (-8x^2)/(x^4-1)

\int \frac{- 8 x ^{2}}{x ^{4} - 1} d x

integral of (2x^3-5x^2+3x-1)

\int (2 x^{3} - 5 x^{2} + 3 x - 1) d x

integral of (x+1/x)^3

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

integral of (sqrt(a^2+u^2))/u

\int \frac{a ^{2} + u ^{2}}{u}

integral of (sin(x)-cos(x))/(sin^2(x))

\int \frac{sin ( x ) - cos ( x )}{sin ^{2} ( x )} d x